LINKS   Hypercube Trailer  .  Time Cube Math  .  The Math of Cube  .  Hypercube by Kaku

..the theory of hyperspace, which states that dimensions exist beyond the commonly accepted four of space and time.  There is a growing acknowledgment among physicists worldwide...that the universe may actually exist in higher-dimensional space.  If this theory is proved correct, it will create a profound conceptual and philosophical revolution in our understanding of the universe."
--Michio Kaku, Hyperspace

"A body is surely less primary being than is its surface; and a surface, than a line; and a line, than a unit or a point.  For a body is defined by these, and they seem able to be without body; whereas a body cannot be without them."
--Aristotle, Metaphysics, book Beta

"But the creative principle resides in mathematics.  In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed."
--Einstein

"The first cube was a formula for death, unless you cracked the code.  But now, terror has a new dimension."
--Trailer for Hypercube


Eventually, we will discuss the limits and benefits of general sciences; we will show them relative to a whole sea of possible sciences, and discuss how much faith we should put in our particular system in the sea of all systems, how much we should cherish our favorite flower, in the field of all possible flowers.

For the moment, however, our only scientific or mathematical discussion will be specifically the application of our theme to higher dimensional space; all our discussion of all this infinite being can be made more clear by devloping a way to view everything in relation to everything else.  We will do three things: show how the scientific theory of hyperspace can be proved by reason alone, consider the applications of an infinitely-dimensioned universe, and begin to apply and map all of (Symmetric) Being into this skeleton template.

[For related reading, I highly suggest the book Hyperspace by Kaku, and the film Cube 2: Hypercube, and any graphing calculator manual].



PROVING HYPERSPACE THEORY VIA REASON

Mathematics graphs various data on a graph of multiple axes, for instance, an x-y-z axis of three dimensions.  When these three are used for length, width, and height, we get space as we generally percieve it.  We can add a fourth axis of time, or a fourth spacial dimension, and use a fifth for time, etc.  The scientific theory of hyperspace observes our world exists beyond the 3D space we percieve.  Some equations make more sense evaluated as part of a higher dimensional world.  Specifically, this theory says there may be ten or twenty-six dimensions.

Our theme, a universe breaking nothingness into infinite life, would not seem to choose some random number of dimensions to stop at.  We will conclude from reason that there are infinite spacial dimensions, and not just space, but we can also place lives, emotions, perceptions, states of being, on this graph, and will develop a system for doing this.  This will give us a template to better understand the scope of our other disciplines, whether this is read before or after the other discussions.

Now science needs experimentation to verify theory.  But experimentation is highly questionable since we have no idea whether to place absolute trust in a system that could be some randomly generated system out of many.  We will therefore conclude that we can deduce all these dimensions by thought alone, just as math and logic exist intrinsically of themselves, needing no experimentation to prove that three times two is six.

Let us start with three dimensional objects, since this is all we're used to dealing with our theories of higher dimensional space (not emotions or states of mind).  Consider a small, red chair in our 3D world.  Consider another similar, large, blue chair.  A four dimensional chair is simply a "stretch of chair" between one and the other -- small red, slightly larger and red-purple, medium sized and purple, somewhat larger and purple-blue, and the large, blue chair, and an infinite set of chairs inbetween.

This construct could mean a few things.  First, it could be considered a single, four-dimensional object, which is somewhat hard for us to understand but still fathomable.  Secondly, it could be the path of a single 3D chair changing through time, morphing by some magical power, or slowly altered by painting it and enlarging it.  Thirdly, it could be an infinite number of 3D chairs, all slightly different. 

(Of course, we could say the same a step downward, that a 3D chair could also be a 2D slice of the chair changing through time, or an infinite handful of 2D chair-slices, etc, though as with four dimensions, a two dimensional object is again hard for us to understand because we mostly associate with a three-dimensional world.)

The observable world around us is all we need to show these exist, we need no scientific proof.  That a single chair transitioning through time to another state is quite clear.  Or that an infinite handful of these chairs exist is also pretty clear.  If we find a few of these in our city: some chairs of various different shades of blue, purple, red, and the sizes we've named, and more in our nation, and more on the whole planet, etc, and observe there are even other planets and whole galaxies of being, surely the number of these similar chairs are infinite.

Our third application of the 4D-stretched chair (the single four-dimensional object), is a little harder to see but still completely deducable.  We often interchange time and the fourth spacial dimension; a single 3D sphere object can clearly be interchanged with a graph of a 2D slice of matter or data moving through a third dimension of time, showing that if the 3D sphere exists, so does a 2D circle moving through time (and can be looked at as something very similar).  Conversely, a graph of an XD object through time can show that a single (X+1)-D object exists.  Therefore, if a 3D chair can move through time, then a single 4D chair must exist.  All we've done with our chair example is basically, to observe a bunch of similarly colored and sized circles, and deduce that a sphere must exist.

Our observations and reasoning to this point are utterly sufficient to prove the entire scientific theory that things might exist in higher dimensions.  If we need any more proof than this, then we should also call for major hard scientific evidence and mathematical proof that the 3D chair right in front of us exists.  We do not need this, it's right there, there's no further need to prove it's basic existence.  All other scientific hyperspace theory is simply a closer examination, applying equations to tiny corners of the chair to prove what is obvious: it's there.  As with unified theories, we see that our theme generates other theories by itself without needing any help from those separate scientific theories.



EXPLORING INFINITELY-DIMENSIONED SPACE-TIME

Having shown a universe with infinite dimensions, we must now thoroughly explore this idea.  Let us start at the bottom with a single point, and accumulate a list of every possible dimensioned object.  Firstly we should consider counting two, three, four, or any countable number of points (or even real numbers such as 1/3 or pi which we shall ignore for now).  Each is more than the other, but none even begins to traverse an infinitesimal stretch of a whole line of points.  We can count forever and will never have traversed a nanometer of a line.

The next step up is a measurable line segment; a finite stretch of points from A to B of a certain length.  Infinitesimally above this is a line segment plus a given integer (one, two, three).  Next is a ray; a starting point plus an infinite stretch from there to infinity.  Next is the ray plus one, ray plus two, etc.  Next is the full 1D line, finally exactly just one dimension more than a point.

And so on.  Line plus any of the former; then a plane segment plane segment (circle, square, or random shape), plane segment plus any of the former, plane-ray (line extended a stretch to infinity), a plane-ray plus any of the former, a plane (2d), and so on for 3D, 4D, 5D, etc.  Then we have certain fractions.  Half of infinity, a third of infinity or a line, infinity minus one dimension, minus two dimensions, etc, which all are not meaningless theoretical number but very exact, real and applicable ratios.

If we go back to our single 3D chair in space, then this whole number system describes all possible handfuls of chairs, all infinite collections, all perhaps moving through one final axis of time (this could mean all chairs staying completely static and unchanging forever through time, or all shifting around exchanging states).  Even more odd to concieve of is the further idea that this entire plethora of objects could in fact seen to be one, single object of infinite dimensions.  If a four or five dimensional object is hard to contemplate, then surely this is even more difficult to comprehend.

Also, we've left something unsaid about this infinitely dimensioned object (or infinite collection of limitedly dimensioned objects); how would we designate these infinite attributes to a chair?  We can start with color, size, shape, location, cost, and so on, but won't we soon run out of attributes?  There is also the matter of the gray area in what we consider a chair; is a slab of wood with three crude legs a sufficient stool?  So wouldn't our object start to branch out to other objects?  A chair of sufficient width becoming a couch, or so thin as to become wall-like, and so on.

In this way, we see that any given object, when extended into enough spacial dimensions, begins to merge with every single other object we're doing the same thing to, where a single object is just some random point on this graph/map of all possible objects, or put more radically, every object in all the universe could be seen as one, single infinitely-dimensioned object!

Now our strange ratios become practical.  If we consider that nothingness has generated infinite things (each thing torn from its perfect invert), and that all objects are related to eachother by a perfectly distributed, infinitely-dimensioned graph, then to consider a fraction of this group is a very real number of objects.  Exactly half are light and half are dark.  All of them collapsed to one less dimension than infinity are all that are exactly one shade, and so forth.  Minus three dimensions (hue, intensity, lightness), are all the chairs that are the exact same color

Considering the ratio that are a single type of object (chair, or television, etc) are much harder, because as we've said the areas are very fuzzy of what we would consider each (a long chair turns into a couch, a computer can be a television, etc).  So to do this, we would somehow have to have a system (that would be too large to ever design) of categorizing exactly what it means to be a chair.



APPLYING INFINITY-D GRAPH TO ALL CONSCIOUSNESS

We have now well explored an infinitely dimensioned graph which we will soon make a chart of after we extend the applications of the graph even further.  We have been discussing objects because they're very familiar in relation to multiple dimensions (i.e. three).  But we can take this whole graphical system and extend it to absolutely all Being: all life, emotion, sensation, perception, knowledge, and so on.

That is, surely a person for a single moment is just like a point, and we can extend this point to a 1D line (our linear lifepath), or  if we ignore time, can choose one single attribute of ourselves, such as eye color, and let the line describe all the exact mes with just a different eye color.  Then other attributes; musical vs nonmusical Socrates; height, intelligence, location, algebraic knowledge, how happy/sad I am, and so on.  As with objects we quickly see us branching out into every fathomable state of consciousness.  The attribute of age extends back into when I was a fetus, and before.  If my body changes enough, I've crossed from human to some animal (surely one can dream one is a dolphin).  If I get a sex change, I've branched into both genders, and so on.

Aristotle tries to reduce that which exists down to it's primary, fundamental elements.  He asks what is primary, and considers material bodies, material elements such as wood, bronze, fire, earth, wind, water, etc, and also points, lines, and planes.  Our answer to this is pretty simple: the universe has torn apart into a sea infinite attributes, all equally balanced and equally fundamental and primary; and points, lines, and planes, are the map of how all these attributes of Being relate.

Similary, in genetics, our DNA tries to divide us into all possible humans (a small chunk of our graph of all life), but is very limited.  For instance, it only describes a finite number of humans; our genetic code is simply a very, very large number in base four.  It's a long series of digits of T, G, A, or C (or in math, 0, 1, 2, or 3).  If this were a billion, this would be saying, "there are exactly a billion potential humans."  Obviously this is not so, surely there are infinite possible humans.  A single finite number cannot even describe a single attribute, such as hair or eye color (there are clearly infinite shades, not a finite number of them).  We would need an infinitely-digited number -- an infinite set of data -- to describe all humans, if we could even agree where to draw the lines on what is human (is a primate human?)

But of course genetics is far from useless, just limited.  It is fascinating that science has discovered one particular system (out of many) of describing a huge spectrum of humans, using just a single number, in the way a digital image is also a large number, a single file of data, not precise and infinitely detailed, but good enough to see what the image is, like DNA to humans.  DNA is just a human (roughly) saved to disc.  And what we'll do here on is continue designing a similar system of our own, to do by reason what DNA does by nature.



CHARTIG WHAT WE'VE EXAMINED

Now that we've explored all these dimensions and applied them, we'll create a chart relating each dimension to those above and below it, but first we need two new terms.  In exploring the idea of infinity, we've clearly seen that some infinities of things are smaller or larger than others.  There are infinite points on a line, but clearly infinite more on a plane, both infinitesimal compared to all points everywhere, etc.  So we'll introduce the idea of "maximum infinity," or "full infinity", the highest possible number fathomable.  In saying all life, we say the maximum infinity of life everywhere, versus what we'll call a  "limited infinity" of some fraction of the maximum, a number somewhere inbetween full infinity and a finite numbers like 7 or 8.

Note these are not absurd, theoretical numbers.  They are mundane and practial.  Our system theorizes that nothingness creates all life, which is half happy and half sad, so the number 1/2 maximum infinity (minus the tiny spec that are neutral, which is one axis less than the infinith axis) is a very important precise number: everyone in the universe who's happy at a given moment (the other half sad).  Knowing this can even be more important (in a way) than knowing the number of people in our city or on our planet.

One more thing we should consider is whether a dimension of length, width, intelligence, color, etc, is stretched out infinitely, or for a measurable, finite span.  If used as time, a line segment can only graph a short duration of a human life, whereas a full line presents an infinite timeline in past and future.  If we use this as an attribute, then a segment can describe only those with blue to green eyes, not all eye hues (in fact we'd need three unlimited dimensions for all color: hue, brightness, and lightness).

More complicated are combinations of various segments or full lines.  A cube (or any normal object) is a point stretched in three measurable segments: 5x5x5, or 5 cubed.  But we could add an infinite axis of time, the lifepath of the cube through eternity, and hence have three "limited" axes and one "unlimited."  Each dimension creates one more category than the last if we're to consider segments as well as unlimited dimensions.  That is, in three dimensions, we could have zero, one, two, or three of those three dimensions limited (the others unlimited), and for four dimensions, we can have zero, one, two, three, or four, creating five object categories apposed to four for 3D, and so oin.

So, from the bottom up, we have a point, integer, line segment (1D pencil, or the border of a circle), a ray, a line (straight, or parabola, etc), shape (circle, square, or random chaotic shape), infinite plane segment (2D toilet paper), plane (flat, or parabolic), normal 3D object (or square through a limited duration), 3D object with one unlimited attribute (neverending pipe), with two unlimited (wall with infinite height and length but not depth), 3 dimensions (space), and so on for higher dimensions.

From the top, we have the maximum infinitely dimensioned graph, all axes unlimited, then one limited, two, etc, down to all limited, then maximum dimensions minus a single axis (all unlimited, then down to all limited), max infinity minus 2, etc.  Then somewhere in the middle of nowhere, below these dimensions and above the finite ones (2D, 3D), we have a limited infinitely dimensioned number of axes, plus or minus any finite number or other limitedly infinite number, of axes, and for each of those, any combination of the infinite axes being limited or unlimited in length.  (It should be noted that the number maximum infinity when applied to maximum dimensions is still a spec in the sea of the maximum number of beings or states, the way I have infinite points on just one single axis, nevermind infinite axes)

After all that, we can apply arithmetic -- addition, subtraction, multiplication, division (fractions) -- to either the number of axes we're talking about, or the individual points or lines, etc.  For instance, 1/2 of all life everywhere [minus the tiny handful of souls who are netural: max dimensions minus one axis, one point (0) on a joy/pain line] are happy at any given moment, and 1/2 sad.  If we have a 1D-stick or a 3D ball, we can then add or multiply to get many sticks or many balls, or, we can add individual points to our 1D-stick, making it infinitesimally longer, and so on. 

[If we were to be tediously thorough and consider the whole plethora of every single one of these categories including ways to alter them arithmetically (calling a full auditorium of people a certain numerical magnitude, and half an auditorium another, half minus any number x another, a single person the lowest, etc etc), we would get (I belive) 10.6 trillion of these categories just in the first five dimensions alone.]

Finally, let us draw up a chart just of just this basic list of axes and describe what they mean or how they can be applied.


DIMENSIONS OF AN INFINITELY DIMESIONED GRAPH;

SYMMETRIC BEING DIVIDED INTO INFINITE ATTRIBUTES

Aristotle said the wise man knows all as far as possible, but nothing in particular. He talks much about classes and attributes, breaks genuses down into subcategories and individuals with precise features.  We have similary shown a way to break down all life and all classes down to the precise individual or object.  It may seem a little odd that something so simple and basic as a point has infinite attributes, but consider that's what a point is, a dot somewhere in vast space-time, than needs a series of coordinats to locate it, such as a point on a large map of many different places, or in space to locate an exact, specific planet in the galaxy.  Our point has not just 2 or three spacial attributes, but infinite, ending up at location that would take infinite data to describe it.

We can note quickly that all of algebra can be applied to this infinitely dimensioned graph, the way that 2D equations can be graphed on an x-y axis, or 3D equations on a 3D graph.  If we have two attributes (height and width, or time and distance, or musical vs nonmusical socrates over time), then our 2D algebraic equations graph onto our 2D plane, showing a single path a soul might take through this other attribute (eye color slowly changing over the course of my life), etc.  And while these paths can be exact and mathematical, our life may also take a chaotic path through this sea of possibility, nonmathematical, buzzing around randomly like a fly or a scribble.

Also, interestly, with algebra and calculus come the notion of intersections: a line in space intersecting a plane at one exact point, a circle within a plane, a cirlce intersecting a plan at a line segment, etc.  Applying this to consciousness, it means another soul and I could intersect at the exact same feeling, except going different directions.  I might be a man living the lifepath he thinks he's living, while another man occupying the exact same mental state might also think he's living my lifepath, but be living a different one (perhaps he's about to wake up from a dream).

We can consider probability.  Let us freeze a single moment.  What are the chances I am exactly neutral?  They're infinitesimal (if we understand that 0 is a point on a line among a whole realm of infinite other joy/pain values).  But is this the same as being zero?  This is tricky.  Even smaller, what if we select one soul in all of infinity to win a lottery?  If all souls everywhere think, alright, this isn't going to be me, but of course one person will indeed be wrong.  Winning this lottery would be infathomably astounding.  No one could ever believe it.  Yet it would happen.  Hence we give a very real meaning to a theoretical number like chances of one in all infinity (whether a small or large infinity).  This is the fraction of myself in all of vast (Symmetric) Being.

One final major wrench we'll throw into this entire system of graphing being is the consideration that perhaps there are actually infinite exact versions of me, or an object.  That since nothigness can break apart into infinite life, then surely some other corner of nothingness has done the exact same thing, and another, etc.  So if this is the case, and there are infinite exact versions of me running around, then we're actually adding one more dimension on top of every other: we have a point, then a set of infinite identical points, then the line of infinite identical lines, etc.

And so now we have taken our theme that all is generated from the rule that joy is rape, and created a large system to enlarge our mind's eye of all the being created from total opposition and how it self-relates, although, we have only barely discussed this system in light of opposition, that is, we have not even considered how our perfect un-self fits into this huge picture, the one thing (a perfect inverse) which has created it all to begin with.  It's been easy to ignore, just as it's a hard thing to fathom in the first place, but we will discuss how this core idea relates to our graphs eventually, casting a better light on everything the way our theme itself casts a new light on life, and have much  more to discuss as well, since there's always infinite more to explore and discuss in regards to science and math, and indeed, everything else.
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