"The LUFE Matrix: Infinite Dimensions © 2004, Reginald Brooks

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.

Ó 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:

(a taunting overview to the works below)

"Naughty Physics (a.k.a. The LUFE Matrix )"

(an advanced view with a brief, but large overview and simple introduction to The LUFE Matrix)

"Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of): The Conservation of SpaceTime by the Conservation of Force"

(the full introduction)

"The LUFE Matrix: The distillation of SI units into more fundamentally base units of Space-Time (ST) dimensions"

(over 200 working examples from easy on up)

"The LUFE Matrix Supplement: Examples and Proofs"

(background material)

"The LUFE Matrix Supplement: References"

I. General: the short answer (click for elaboration)

1. Are there more than 3 space and 1 time dimensions? Yes.

2. If yes, how many dimensions are there? Infinite.

3. Are dimensions absolute or relative? Relative.

4. Are any/all of the multiple space dimensions interchangeable? Yes.

5. Are any/all of the multiple time dimensions interchangeable? Yes.

6. Can we directly isolate and measure, with our own senses or instruments, more than 3 space and 1 time dimensions? No, not without changing our current conceptions, and therefore, our perceptions of measurement.

7. Does space or time exist independently? No.

8. Does that mean you can only experience space or time by invoking the other as the clock or ruler? Yes.

9. If yes, does that mean that motion...be it that of movement, formation or transformation...is the basis for what we mean and now newly define as dimension? Yes.

10. So if all dimension is motion and all motion is fundamentally constructed from the relative interaction of space and time entities, or areas...areas which are not real, but virtual pointers...then should not our conception of "dimension" be redefined as the "Space Time Interactional Dimension (STID)" composed of multiple (at least one of each), virtual pointers of "Space Or Time Areas (SOTA)"? Yes.

11. Can we still, for ease of use, refer to these isolated, abstract space or time areas (SOTA) simply as "space dimensions" or "time dimensions", instead of the newer, but more cumbersome "space virtual pointer" or "time virtual pointer" dimension; and, likewise, can we also simply refer to the "Space Time Interactional Dimension (STID)" as the new "ST dimension". Yes.

12. Is there a simple, functional graphical presentation in which the new conception of ST dimensions (STIDs), formed from the interaction of individual space or time areas (SOTAs)...or space or time dimensions, if you prefer...is laid out in a clear and concise way which accounts for both multiple, even infinite, number of dimensions and for the very real physical parameters like velocity, mass, charge, momentum, spin, energy...etc. which exists as the consequence of that space and time interaction? Yes, it's called The LUFE Matrix and the diagrammatic chart symbolically illustrating those dimensions is called The LUFE Matrix: Infinite Dimensions Chart referenced below.

II. General: elaboration (click # to return to short answer above)

1. & 2. Our past conception of time and space, based on our anthropocentric view of nature, places man, woman and child at the center and measure of the universe. Initially space was like an absolute, perfect box in 3 dimensions with a single clock ticking at the same frequency for eternity. Our new conception of ST dimensions extends this to at least 25, perhaps infinite dimensions.

3. Although relativity started at least with Galileo, and probably well before, Einstein showed us both formally with mathematics, and especially conceptionally with his visualizations, that time is not absolute, and therefore, neither is the space which takes time to measure, and as such, time must be included as a dimension right along side the 3 axis' of space. His Special Theory of Relativity of uniform motion in 1905 established the reciprocal expansion/contraction of space and time relationship allowing for, indeed demanding, the constancy of the velocity of light. In 1915, he extended this concept to non-uniform motion (acceleration = gravity-mass) in his General Theory of Relativity. Now, every ruler and every mass is effected by the clock...and the clocks are relative, too, to the energy of the system they are in. Thus a ruler or mass will contract under high energy as measured by a clock under that same energy system. They will contract differently when the clock is in a different energy system. Time is dilated...that is the ticking of the clock is slowed...as the energy of the system is increased. Expanding upon and completely congruent with Einstein's conception of the interdependence of space and time are the ST dimensions of The LUFE Matrix. Expanded upon, as now we have multiple space dimensions interacting with multiple time dimensions. Congruency follows as the co-dependence of the Space Time Interactional Dimensions (STIDs) formed, as each SOTA behaves as a single, relative contributor to the overall mix establishing the identity of the resultant STID formed. HINT: In our new conception, not only are there more than 3 dimensions of space, there are also more than 1 dimensions of time.

4. Each space virtual area, or pointer dimension, is like every other and is thus interchangeable. One space dimension acts like a conventional line, two like an area, three like a volume, etc. Take away one space dimension from a volume and you have a net area, take away two and you have a net line. But what about the "etc.?" What does 4 or 5 dimensional space look like? Hold on, we're coming to that!

5. Similarly, each time virtual area, or pointer dimension, is like every other and is thus interchangeable. Again hold on, but here's another HINT: In the S/T quadrant of The LUFE Matrix, each successive time dimension is invoked when the previous parameter is now expressed as a function of a new time...that is, as per a new unit of time. For Example, velocity is meters per second or meters/sec or m/s. Acceleration, which is a change in velocity, is expressed as velocity/second. If you break it down it becomes meters/sec/sec or m/s/s or m/s². In other words, velocity is 1 space dimension/1 time dimension and acceleration is 1 space dimension/2 time dimensions.

6. In our past conception of space and time dimensions it appears that we can locate any object in the universe if we know its x-, y- and z- axis location points and the time interval. This conceit presupposes a still somewhat classical (anthropocentric) and typically absolute, or near absolute, view of space, with the relativity of spacetime invoked only under unusual, very high energy conditions. In our new conception of ST dimensions, picture our classical 3 dimensional space +1 dimensional time as a room...a room with a view. Let's call this the mid room. Now, looking out the window of the room with a view with our cosmoscope, we see that we are but a speck of dust on the floor of another very large room...it too, with a view. In the big room there also exists a classical 3D space + 1D time. And of course, there is a very small room with a view, with its own classical 3D space + 1D time, and when they look out their window with their cosmoscope they see us in our mid room. A series of a room with a view within a room with a view within a room with a view...and so on. In this telescoping view of ST dimensions it is easy to see how each small, mid and large reference rooms could sense and measure their views as being limited to, and completely consistent with, a single 3D space + 1D time view...similar to what we have shared for nearly 100 years. Never seeing the relativeness of their own measurement system, their conclusions would seem to be logical and ill refutable. As an extension to Einstein's Relativity, once you place yourself outside a single, inertial reference system and compare your conclusions with what is found inside that single, inertial reference system, you will find the answer...the location, measurement and time intervals of your points of interest…is entirely dependent on the location and energy signature of the reference system utilized to make those determinations. The clocks and rulers of the small, mid and large rooms, as well as the essentially infinite scales of rooms in between, will also be true and essentially "absolute" to themselves in terms of 3D space +1D time dimensions. And in many situations they will be remarkably consistent with many other rooms with either similar or simple harmonic interval differences in energy signature. It is only in such absolute inertial reference systems that the illusion of a past, present and future can be maintained.

7. Extension of space creates times. Contraction of space slows time down. Without space extension, there is no time. The flip side to this coin is that time creates space extension. Dilating the time...which means reducing its frequency...contracts the space.

8. Time is the inverse of frequency (n ) as t=1/n . Frequency is the cycles per second (or other unit of time). Cycles of what? Something that rotates, pulses, is created or transformed. Fundamentally, at the level of space and time creation, spatial extension is that which pulses...it cycles. It comes into being, then out, then into being, and out over and over as a cyclic frequency of presentation. Its presence creates the clock...the time. Remove the space and you remove the time...and vice versa. ST pulses. (NOTE: Not to confuse the situation, you should also be aware of the intimate relationship between time, frequency and temperature (T). As frequency equals temperature, time is also the inverse of the temperature, as t=1/n =1/T or T=n =1/t.) The same is true for the space dimensions. Like time, they can exist as virtual pointer or place-holder dimensions, largely as either potential components to add to the STID areas or as containers to "hold" some of the physical STID parameters denuded of some space or time dimensions by a transaction or interaction. Thus a wavelength (8) of light exists as 1 unit of space virtual pointer dimension, but only exists as a true ST interactional dimension (STID) when it interacts with a time virtual pointer dimension, forming c=8n , the velocity of light (c).

9. Without a question, yes! As there is no static room with a view anywhere in the universe, it is the interactional dynamic of space forming along any number of x- and/or y- and/or z-axis per unit(s) of time...a cyclic pulse generation...that spacetime itself is formed of the action of motion. An action that occurs rhythmically, often simultaneously, in each of one or more rooms with a view that defines the multi-dimensional universe. For more on this see "Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of)"

10-12. Historically, we have tried to separate space from time. Early last century we learned to add back the time dimension. Later, we learned through our mathematics that additional dimensions were possible and logically required to explain the universe. "The LUFE Matrix, first introduced in 1985, is a model of a multi-dimensional spacetime universe in which the physics of matter and fields are formed from, and exist in, the very spacetime interactional dimensions of which they are composed. In this century, we are now ready to "see" those multiple, perhaps infinite, dimensions! For many, many working examples and proofs (over 200) please see "The LUFE Matrix Supplement".

III. Details

1. Why does it appear that there are only 3D of space and 1D of time dimensions?

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.

2. Would not a simple shift in the position of our room, or moving to yet another room with a view reveal additional perspectives?

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.

3. Would not a comparison of these various perspectives inform, combine, commensurate and generate a consensus that all such views from all rooms will reveal the same 3D space + 1D time dimension universe that we seem to be living in?

Yes.

4. So what's the problem? Why do we need to have more dimensions?

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 Space-Time 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 Space-Time 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 (T₀...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/s²), 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 (x-axis), adding a second space dimension invokes the y-axis and a 2D area is formed. Adding yet another 1D space dimension along the z-axis 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 Multi-Dimensions...and so should be designated as 3D space + MD time dimensions hereafter. (Yes Dr.Time can fix your time.)

5. After reviewing #1.-#4. I'm still not getting it. What's missing here? It seems you have argued for the existence of ordinary 3D space + time dimensions?

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 relativity-based 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 Dark-Dark-Light 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 z-axis of the new, larger room with a view, which is itself undergoing a pulse generation to form its x-, y-, or z-axial 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 x-axis of the subset room matches the orientation of the x-axis 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 catch-22 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.

6. What are the similarities and differences between each of the space dimensions?

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 z-axis, 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 x-axis 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 x-plane as the reference to which all other axial planes refer.).

2D is diagrammatically represented as a second line, along the y-axis and perpendicular to the x-axis, 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 Z-axis 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.

7. What are the similarities and differences between each of the time 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 z-axis, 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 2-segment line=2D and a 3-segment line=3D...and so on as you progress down any given column.

The next three questions are crucial...so hang on!

8. What happens when you have a lot more of one dimension than other?

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.

9. When the space dimension line(s) pulsates (cycles), what time dimension is associated with what space dimension?

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 z-axial 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 z-spatial 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 2-segmented line and the third as a 3-segmented 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.

10. Are the space or time dimensions vectors or scalars?

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.

This paper and all its contents © 2004, Reginald Brooks. All rights reserved. Permission is hereby granted for single copies to be made for personal, non-commercial 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.

The LUFE Matrix Operational Rules (See the graphic below.)This is part of The LUFE Matrix: Introduction-Geometry-Layout-Rules 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 area on the matrix defines the physical entity and its units of expression. Interactional ST dimensions have areas within a quadrant, while purely spatial or temporal dimensions have linear "spaces" along their respective axis. The identity of a physical entity, be it a quantity or the units to describe/measure it, in terms of net amounts of so much spatial dimension and/or temporal dimension is constant and does not change regardless of its operation location on the matrix.

All net areas and spaces are counted from the origin, 0, where the x-(space) and y-(time) axial coordinates cross.

Pure spatial (like length) or temporal (like time, frequency or temperature) dimensions never appear by themselves in a quadrant. They are confined to their static, linear space on the axis. These are referred to as Space Or Time Areas (SOTA). Pure spatial dimensions always go to infinity in both the up and down directions for each spatial dimension. Pure temporal dimensions always go to infinity in both the left and right direction for each temporal dimension. Each is like a bipolar laser.

It is only in perpendicular combination(s) that space and time dimensions dynamically interact to form ST interactional dimensions (STID).

Once you are on the matrix proper, that is on the STID area, then the multiplication (by addition) or division (by subtraction) of any other dimensions, be they ST interactional dimensions or pure spatial or temporal dimensions, is begun from that area already defined on the matrix at that point (not from the origin, 0), using its usual ST designation. For example, acceleration (S_I/T_II) is velocity (S_I/T_I) per unit of time (T_I), so if velocity is first located on the matrix at the S_I/T_I ST interactional area of the S/T quadrant, then dividing this per unit of time (T_I), which is the same as multiplying it by 1/T _I, requires in this case that we add one unit of pure temporal dimension (1/T_I ) to the existing S_I/T_I STID area to give acceleration (S_I /T_I · 1/T_I = S_I/T_II).

Tip: Get on the matrix proper first with the larger STID areas, then combine the smaller STID units and/or pure SOTA units. Remember to keep the distinction between SOTA and STID areas clear in mind during all operations. Each is composed of pure dimensions that run to infinity, but only STID areas have both space and time dimensions. Once we get into the mathematical equations, all of which can be simplified and solved on the matrix, we will then begin to add and/or subtract various SOTA and STID areas to others already on the matrix. This entails building out (for multiplication we add areas) or in (for division we subtract areas) as the equations are solved. SOTAs are added or subtracted to the grid row or column, to which their bipolar, laser-light-like influence extends, thus they act next to the sides of an existing area. On the other hand, STID areas are added or subtracted diagonally to other STID areas. This is only natural as the STID areas have their dual, perpendicular, bipolar, laser-light-like influence going both horizontally and vertically.

Only physical entities that have net dimensional quantities appear on the matrix or are involved in any of the operations of the matrix. Dimensionless units include any pure numbers, integers, fractions, geometric ratios, radians, trigonomic, logarithmic, or other functions, and the like. In short, any units such that when their SI units are converted to ST units and there remains no net ST units then such entities are dimensionless units. Examples include Newton's gravitational constant, Coulomb's constant, the permittivity of free space, the dielectric constant and the fine structure constant.

The LUFE Matrix readily displays the dynamics of mathematical operations involving the multiplication or division of physical entities. Addition or subtraction does not effect the matrix, nor does the order in which mathematical operation take place. It is only the net, remaining area (or linear space) that counts.

Multiplication in the matrix is akin to exponential multiplication…the product of two or more dimensional quantities is found by the addition of their dimensional designations. Two examples: S_I · S_IV = S_V, and, S_I/T_I · S_IV/T_III= S_V/T_IV.

Division is similar to exponential division…the quotient of two or more dimensional quantities is found by the subtraction of their dimensional designations. Two examples: S _V/T_IV ¸ 1/T_I = S_V/T_III, and (S_III/T_II)² ¸ (S_I)² = S_IV/T_IV.

The LUFE Matrix is equally valid for the MKS, CGS and other less universal systems of units as the idea is to reduce and distill these systems to one in which there are only two fundamental base units, space and time.

The LUFE Matrix Graphic Dynamics

Digital version for the computer: grays-inactive , color-active

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 x-axis, graded in grays, to represent the pure "space" axis. Then we add the vertical y-axis 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.

~hover your cursor over the highlighted text to show its matrix location~

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~

~best viewed 800x600, ~toggle F11 for full image
Axes
#	*description*	*ST unit*
1	space axis	-
2	time axis added	-
3	axes in color	-
4	grid boxes added	-
5	text added to boxes	-

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 #6-10 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~

[ TOP ]
Quadrants
#	description	ST unit

6	ST quadrant	-
7	S/T quadrant	-
8	1/(ST) quadrant	-
9	T/S quadrant	-
10	all quadrants	-

Working Color Template

To make the color work for us a little better, we tried adding the blue-green 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~

[ TOP ]
Color Templates
#	*description*	*ST unit*
11	initial color model	-
12	discreet color model	-
13	working color template	-

NEXT: On to Page 6a- Geometry-Layout-Rules

________________________________________________________

Page 6a- Geometry- Layout

Page 6b- Geometry- Space Or Time Area (SOTA)

Page 6c- Geometry- Space-Time 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: Introduction-Layout & Rules

Page 7c- The LUFE Matrix Supplement: References

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