SYMMETRICBEING: Math& Hyperspace
LINKS Hypercube Trailer . Time Cube Math . The Math of Cube . Hypercube by Kaku
..thetheory of hyperspace, which states that dimensions exist beyond thecommonly accepted four of space and time. There is a growingacknowledgment among physicists worldwide...that the universe mayactually exist in higher-dimensional space. If this theory isproved correct, it will create a profound conceptual and philosophicalrevolution in our understanding of the universe."
--Michio Kaku, Hyperspace
"A body is surely less primary being than is its surface; and asurface, than a line; and a line, than a unit or a point. Forabody 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 acertainsense, therefore, I hold it true that pure thought can grasp reality,as the ancients dreamed."
"The first cube was a formula for death, unless you cracked thecode. But now, terror has a new dimension."
--Trailer for Hypercube
Eventually,we will discuss the limits and benefits of general sciences; we willshow them relative to a whole sea of possible sciences, and discuss howmuch faith we should put in our particular system in the sea of allsystems, how much we should cherish our favorite flower, in the fieldof all possible flowers.
For the moment, however, our only scientific or mathematical discussionwill be specifically the application of our theme to higher dimensionalspace; all our discussion of all this infinite being can be made moreclear by devloping a way to view everything in relation to everythingelse. We will do three things: show how thescientifictheory of hyperspace can be proved by reason alone, consider theapplications of an infinitely-dimensioned universe, and begin to applyand map all of (Symmetric) Being into this skeleton template.
[For related reading, I highly suggest the book Hyperspace by Kaku, andthe film Cube 2: Hypercube, and any graphing calculator manual].
PROVING HYPERSPACETHEORY VIA REASON
Mathematics graphs various data on a graph of multiple axes, forinstance, an x-y-z axis of three dimensions. When these threeareused for length, width, and height, we get space as we generallypercieve it. We can add a fourth axis of time, or a fourthspacial dimension, and use a fifth for time, etc. Thescientifictheory of hyperspace observes our world exists beyond the 3D space wepercieve. Some equations make more sense evaluated as part ofahigher dimensional world. Specifically, this theory saystheremay be ten or twenty-six dimensions.
Our theme, a universe breaking nothingness into infinite life, wouldnot seem to choose some random number of dimensions to stopat. We will conclude from reason that there are infinite spacialdimensions, and not just space, but we can also place lives, emotions,perceptions, states of being, on this graph, and will develop a systemfor doing this. This will give us a template to betterunderstandthe scope of our other disciplines, whether this is read before orafter the other discussions.
Now science needs experimentation to verify theory. Butexperimentation is highly questionable since we have no idea whether toplace absolute trust in a system that could be some randomly generatedsystem out of many. We will therefore conclude that we candeduceall these dimensions by thought alone, just as math and logic existintrinsically of themselves, needing no experimentation to prove thatthree times two is six.
Let us start with three dimensional objects, since this is all we'reused to dealing with our theories of higher dimensional space (notemotions or states of mind). Consider a small, red chair inour3D world. Consider another similar, large, bluechair. Afour dimensional chair is simply a "stretch of chair" between one andthe other -- small red, slightly larger and red-purple, medium sizedand 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 beconsidered a single, four-dimensional object, which is somewhat hardfor us to understand but still fathomable. Secondly, it couldbethe path of a single 3D chair changing through time, morphing by somemagical power, or slowly altered by painting it and enlargingit. Thirdly, it could be an infinite number of 3D chairs, all slightlydifferent.
(Of course, we could say the same a step downward, that a 3D chaircould also be a 2D slice of the chair changing through time, or aninfinite handful of 2D chair-slices, etc, though as with fourdimensions, a two dimensional object is again hard for us to understandbecause we mostly associate with a three-dimensional world.)
The observable world around us is all we need to show these exist, weneed no scientific proof. That a single chair transitioningthrough time to another state is quite clear. Or that aninfinitehandful of these chairs exist is also pretty clear. If wefind afew of these in our city: some chairs of various different shades ofblue, 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 otherplanets and whole galaxies of being, surely the number of these similarchairs are infinite.
Our third application of the 4D-stretched chair (the singlefour-dimensional object), is a little harder to see but stillcompletely deducable. We often interchange time and thefourthspacial dimension; a single 3D sphere object can clearly beinterchanged with a graph of a 2D slice of matter or data movingthrough a third dimension of time, showing that if the 3D sphereexists, so does a 2D circle moving through time (and can be looked atas something very similar). Conversely, a graph of an XDobjectthrough time can show that a single (X+1)-D object exists. Therefore, if a 3D chair can move through time, then a single 4D chairmust exist. All we've done with our chair example isbasically,to observe a bunch of similarly colored and sized circles, and deducethat a sphere must exist.
Our observations and reasoning to this point are utterly sufficient toprove the entire scientific theory that things might exist in higherdimensions. If we need any more proof than this, then weshouldalso call for major hard scientific evidence and mathematical proofthat the 3D chair right in front of us exists. We do not needthis, it's right there, there's no further need to prove it's basicexistence. All other scientific hyperspace theory is simply acloser examination, applying equations to tiny corners of the chair toprove what is obvious: it's there. As with unified theories,wesee that our theme generates other theories by itself without needingany help from those separate scientific theories.
Having shown a universe with infinite dimensions, we must nowthoroughly explore this idea. Let us start at the bottom withasingle point, and accumulate a list of every possible dimensionedobject. Firstly we should consider counting two, three, four,orany countable number of points (or even real numbers such as 1/3 or piwhich we shall ignore for now). Each is more than the other,butnone even begins to traverse an infinitesimal stretch of a whole lineof points. We can count forever and will never have traversedananometer of a line.
The next step up is a measurable line segment; a finite stretch ofpoints from A to B of a certain length. Infinitesimally abovethis is a line segment plus a given integer (one, two,three). Next is a ray; a starting point plus an infinite stretch from there toinfinity. Next is the ray plus one, ray plus two,etc. Nextis the full 1D line, finally exactly just one dimension more than apoint.
And so on. Line plus any of the former; then a plane segmentplane segment (circle, square, or random shape), plane segment plus anyof the former, plane-ray (line extended a stretch to infinity), aplane-ray plus any of the former, a plane (2d), and so on for 3D, 4D,5D, etc. Then we have certain fractions. Half ofinfinity,a third of infinity or a line, infinity minus one dimension, minus twodimensions, etc, which all are not meaningless theoretical number butvery exact, real and applicable ratios.
If we go back to our single 3D chair in space, then this whole numbersystem describes all possible handfuls of chairs, all infinitecollections, all perhaps moving through one final axis of time (thiscould mean all chairs staying completely static and unchanging foreverthrough time, or all shifting around exchanging states). Evenmore odd to concieve of is the further idea that this entire plethoraof objects could in fact seen to be one, single object of infinitedimensions. If a four or five dimensional object is hard tocontemplate, then surely this is even more difficult to comprehend.
Also, we've left something unsaid about this infinitely dimensionedobject (or infinite collection of limitedly dimensioned objects); howwould we designate these infinite attributes to a chair? Wecanstart with color, size, shape, location, cost, and so on, but won't wesoon run out of attributes? There is also the matter of thegrayarea in what we consider a chair; is a slab of wood with three crudelegs a sufficient stool? So wouldn't our object start tobranchout to other objects? A chair of sufficient width becoming acouch, or so thin as to become wall-like, and so on.
In this way, we see that any given object, when extended into enoughspacial dimensions, begins to merge with every single other objectwe're doing the same thing to, where a single object is just somerandom point on this graph/map of all possible objects, or put moreradically, every object in all the universe could be seen as one,single infinitely-dimensioned object!
Now our strange ratios become practical. If we consider thatnothingness has generated infinite things (each thing torn from itsperfect invert), and that all objects are related to eachother by aperfectly distributed, infinitely-dimensioned graph, then to consider afraction of this group is a very real number of objects. Exactlyhalf are light and half are dark. All of them collapsed tooneless dimension than infinity are all that are exactly one shade, and soforth. Minus three dimensions (hue, intensity, lightness),areall the chairs that are the exact same color
Considering the ratio that are a single type of object (chair, ortelevision, etc) are much harder, because as we've said the areas arevery fuzzy of what we would consider each (a long chair turns into acouch, a computer can be a television, etc). So to do this,wewould somehow have to have a system (that would be too large to everdesign) of categorizing exactly what it means to be a chair.
APPLYING INFINITY-DGRAPH TO ALL CONSCIOUSNESS
We have now well explored an infinitely dimensioned graph which we willsoon make a chart of after we extend the applications of the graph evenfurther. We have been discussing objects because they're veryfamiliar in relation to multiple dimensions (i.e. three). Butwecan take this whole graphical system and extend it to absolutely allBeing: all life, emotion, sensation, perception, knowledge, and so on.
That is, surely a person for a single moment is just like a point, andwe can extend this point to a 1D line (our linear lifepath),or if we ignore time, can choose one single attribute of ourselves, suchas eye color, and let the line describe all the exact mes with just adifferent eye color. Then other attributes; musical vsnonmusicalSocrates; height, intelligence, location, algebraic knowledge, howhappy/sad I am, and so on. As with objects we quickly see usbranching out into every fathomable state of consciousness. Theattribute of age extends back into when I was a fetus, andbefore. If my body changes enough, I've crossed from human tosome animal (surely one can dream one is a dolphin). If I getasex 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 considersmaterial bodies, material elements such as wood, bronze, fire, earth,wind, water, etc, and also points, lines, and planes. Ouranswerto this is pretty simple: the universe has torn apart into a seainfinite attributes, all equally balanced and equally fundamental andprimary; and points, lines, and planes, are the map of how all theseattributes of Being relate.
Similary, in genetics, our DNA tries to divide us into all possiblehumans (a small chunk of our graph of all life), but is verylimited. For instance, it only describes a finite number ofhumans; our genetic code is simply a very, very large number in basefour. It's a long series of digits of T, G, A, or C (or inmath,0, 1, 2, or 3). If this were a billion, this would be saying,"there are exactly a billion potential humans." Obviouslythis isnot so, surely there are infinite possible humans. A singlefinite number cannot even describe a single attribute, such as hair oreye color (there are clearly infinite shades, not a finite number ofthem). We would need an infinitely-digited number -- aninfiniteset of data -- to describe all humans, if we could even agree where todraw the lines on what is human (is a primate human?)
But of course genetics is far from useless, just limited. Itisfascinating that science has discovered one particular system (out ofmany) of describing a huge spectrum of humans, using just a singlenumber, in the way a digital image is also a large number, a singlefile of data, not precise and infinitely detailed, but good enough tosee what the image is, like DNA to humans. DNA is just ahuman(roughly) saved to disc. And what we'll do here on iscontinuedesigning a similar system of our own, to do by reason what DNA does bynature.
CHARTING WHAT WE'VE EXAMINED
Now that we've explored all these dimensions and applied them, we'llcreate a chart relating each dimension to those above and below it, butfirst we need two new terms. In exploring the idea ofinfinity,we've clearly seen that some infinities of things are smaller or largerthan others. There are infinite points on a line, but clearlyinfinite more on a plane, both infinitesimal compared to all pointseverywhere, etc. So we'll introduce the idea of "maximuminfinity," or "full infinity", the highest possible numberfathomable. In saying all life, we say the maximum infinityoflife everywhere, versus what we'll call a "limited infinity"ofsome fraction of the maximum, a number somewhere inbetween fullinfinity and a finite numbers like 7 or 8.
Note these are not absurd, theoretical numbers. They aremundaneand practial. Our system theorizes that nothingness createsalllife, which is half happy and half sad, so the number 1/2 maximuminfinity (minus the tiny spec that are neutral, which is one axis lessthan the infinith axis) is a very important precise number: everyone inthe universe who's happy at a given moment (the other halfsad). Knowing this can even be more important (in a way) than knowing thenumber 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 ameasurable, finite span. If used as time, a line segment canonlygraph a short duration of a human life, whereas a full line presents aninfinite timeline in past and future. If we use this as anattribute, then a segment can describe only those with blue to greeneyes, not all eye hues (in fact we'd need three unlimited dimensionsfor all color: hue, brightness, and lightness).
More complicated are combinations of various segments or fulllines. A cube (or any normal object) is a point stretched inthree measurable segments: 5x5x5, or 5 cubed. But we couldadd aninfinite axis of time, the lifepath of the cube through eternity, andhence have three "limited" axes and one "unlimited." Eachdimension creates one more category than the last if we're to considersegments as well as unlimited dimensions. That is, in threedimensions, we could have zero, one, two, or three of those threedimensions limited (the others unlimited), and for four dimensions, wecan have zero, one, two, three, or four, creating five objectcategories apposed to four for 3D, and so oin.
So, from the bottom up, we have a point, integer, line segment (1Dpencil, or the border of a circle), a ray, a line (straight, orparabola, 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 withone unlimited attribute (neverending pipe), with two unlimited (wallwith 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, allaxes unlimited, then one limited, two, etc, down to all limited, thenmaximum dimensions minus a single axis (all unlimited, then down to alllimited), max infinity minus 2, etc. Then somewhere in themiddleof nowhere, below these dimensions and above the finite ones (2D, 3D),we have a limited infinitely dimensioned number of axes, plus or minusany finite number or other limitedly infinite number, of axes, and foreach of those, any combination of the infinite axes being limited orunlimited in length. (It should be noted that the numbermaximuminfinity when applied to maximum dimensions is still a spec in the seaof the maximum number of beings or states, the way I have infinitepoints 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 axeswe're talking about, or the individual points or lines, etc. Forinstance, 1/2 of all life everywhere [minus the tiny handful of soulswho are netural: max dimensions minus one axis, one point (0) on ajoy/pain line] are happy at any given moment, and 1/2 sad. Ifwehave a 1D-stick or a 3D ball, we can then add or multiply to get manysticks 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 ofevery single one of these categories including ways to alter themarithmetically (calling a full auditorium of people a certain numericalmagnitude, and half an auditorium another, half minus any number xanother, a single person the lowest, etc etc), we would get (I belive)10.6 trillion of these categories just in the first five dimensionsalone.]
Finally, let us draw up a chart just of just this basic list of axesand describe what they mean or how they can be applied.
DIMENSIONS OF ANINFINITELY DIMESIONED GRAPH;
SYMMETRIC BEING DIVIDED INTO INFINITE ATTRIBUTES
|maximum infinitely dimensioned graph||The greatest graph possible, maximuminfiniteaxes, all also extended infinitely, on which we can put all soulsand/or all objects and/or all feelings or states of consciousness, inall of existence, or possibly consider all this one single,infinitely-dimensioned thing. Our version of "space-time,"exceptall being instead of just space. Philosophy calls this Being(except perhaps "Being" could refer to something more, like the fieldof calculus whether or not anyone is percieving it).|
1 limited axis
|Still maximum infinite axes, withjust onesingle axis stretched a limited span. This could be all ofbeing,from nine this morning to friday at midnight. Or if the oneshortaxis is color, then all in existence that's anywhere from green to blue.|
2 limited axes
|Maximum infinite axes, with twostretching afinite span instead stretched out forever. This could be thesingle joy/pain axis and the single time axis (two very special axes)being limited, which would mean the lifepath of everyone in existencewho's between 6.3 units happy to 4 units sad, from nine this morning tofriday at midnight. Or everything in existence that's betweenredto orange, from nine this morning until midight friday. Or anobject with all infinite dimensions except for a limited, measurablewidth and length.|
3 limited axes
|All souls that are blue to green,from monday to Friday, that are from 6.4 happy to 4 sad.|
|Still maximum number of axes, butthe strangenumber half of those axes limited, half unlimited. We couldofcourse have other fractions.|
| Three unlimited attributesand all others limited.|
|- A single, infinitely-sided cube,colored any white to any black, plus time.|
- All limited attributes except one infinite.
|- A single, infinitely-sided cube,plus an entire axis of time.|
- A single, infinitely-sided cube, colored any white to any black
- All attributes of being, limited, except one on an infinite span.
all limited axes
|On the low bottom of the infiniteset of graphsof maximum possible axes, the one with all limited axes. Thisisa single, normal, infinitely-dimensioned object. Just as wecanhave a 7x7x7x7 hypercube (seven to the fourth), an infinitelydimensioned cube would be x to the infinith (all equal sides), or somerandom rectangular hyperbox, each side some different length. Orthe full, infinite set of attributes of consciousness, but only alimited span of each (the blue to green, 4.5 happy to 8 sad, genius tomildly intelligent (and so on for every single fathomable attribute),monkeys to men, etc.|
|max inf - 1D; all unlimited axes||The topmost category for just oneless axis thanthe maximum possible, all of those axes infinite from horizon tohorizon. This is all the souls inexistence who havea totally neutral mood (while everyone else is happy or sad) for anygiven exact moment. We say that half of all the given soulsinexistence are happy and half sad at a given moment, minus this axis ofneutral souls. So happy or sad souls are (1/2 Max-inf) -(Max-Inf-1D). Or, we could say all souls at any givenjoy/painvalue (all at pi pain), or all souls that are exactly one hue of blue.|
|max inf - 1D; 1 limited||All the souls in existence, minus anentire axis(time, or joy/pain, etc), then one attribute (axis) of which onlyincludes a limited span, i.e. all the neutral, red to orange souls inexistence.|
|max inf - 1D;|
|All the neutral, red to orange lifewith IQ of 60 to 80.|
|max inf - 1D;|
|this line has been left blank dueto beeing up for over 20 hours andbecause of the desire to put a bullet in my head if i have to bend mybrain around higher dimensional space for another moment|
|max inf - 1D;|
|this line has been left blank dueto beeing up for over 20 hours andbecause of the desire to put a bullet in my head if i have to bend mybrain around higher dimensional space for another moment|
|max inf - 2D; all unlimited||All life minus two axes: i.e. allneutral, orange-hued souls.|
|max inf - 2D; 1 limited||All neutral, orange-hued souls, withIQ of 60 to 80, and so on.|
|max inf - 2D;|
|Some random number of infinite axes,far belowthe graph of the maximum number of axes, and far above 1D, 2D, etc,where each attribute is extended infinitely.|
We can get here by starting with everything and subtracting oneattribute then another, limiting our categories (all orange souls, allorange neutral souls, all orange neutral souls of IQ 45), passingthrough this and eventually narrowing down to a single exact feeling atthe very bottom of infinite description, or we could start at thebottom and add each attribute, start with the infinitely specific andwork through here up to the top.
Or, a single object of uncountable dimensions, but to which still couldbe added infinitely more sides. And so on for allcombinations oflimited or unlimted axes for this exact number of axes, and for allcombinations of limited or unlimted axes for all closeby neighbors ofthis number of axes (Lim-Inf-D - 1D, etc)
| ....|| ....|
|5D 3 unlim|| ....|
|5D 2 unlim|| ....|
|5D (one unlim axis)|| ....|
|basic 5D object||- one single, normal fivedimensional object|
- 4D space from noon to midnight
- 5 limited attributess
|4D space||- what we call space-time (3D spaceplus time), or, vast four dimensional space.|
- an object with four unending dimensions, or four attributes, etc.
|4D segment (3 unlim. axes)||- all real, happy or sad numbersfrom blue to green and any brightness|
- 3D space from tuesday to friday
- any three extended attributes of being plus time
- a 3D graph of data plus one more limited axis
|4D chunk (2 unlim. axes)||- The neverending lifepath of anevernding pipe|
- A four dimensional object of limited width and height and
- an object of finite length and width but infinite depth and 4thspacial dimension, or time
- Four unending attributes and two limited
- two unending attributes, one limited, plus a limited period of time
- lifepath of an infinitely wide and long wall from monday to wedensday.
|4D chunk (1 unlim axis)||- normal 3D object's unendinglifepath.|
- 3D object plus an infinite attribute.
- all real numbers colored blue to green, a given white to a givenblack, from a fgiven joy level to a given pain level.
- the lifepath of an unending, 3D pipe from monday to sunday.
|basic 4D object||- a hypercube.|
- a 3D-object's lifepath from wednesday to suday.
- a 3D object plus some other limited attribute. Or fourlimited attributes, etc
|3D space||- The physical 3D space all around us|
- a single 3D object with infinite length, width, height.
- the infinite lifepath of Bob the Square
- three unlimited attributes (any real number, any hue, any brightness).
- any graph of 3D data.
|3D segment (two unlim. axes)||all real numbers that are any shadeof any blackto any white with a hue of only blue to green. A wall ininfiniteheight and length, but not depth.|
|3D segment (one unlim. axis)||An infinitely long 3D pipe, or theattributesblue to green and happy measurement 1 to happy measurement 0.7,extended through time, etc.|
|3D object||3 dimensions, each a finite span. Anynormal 3D object, or 2D object plus time, or three finite attributes ofbeing, or two finite attributes (blue to green, five to seven) plustime, etc.|
|2D plane||Two attributes extended infinitely:all theMusical and Intelligent Socrates vs the more and more (or less andless) musical and intelligent. Or, a single infiniteattribute(all the happy or sad mes) extended along an infinitetimeline. Or a single 2D object with infinite width and height. Or aseriesof all real numbers, each colored any shade from pure white to infiniteblack. Or any given graph of data (acceleration vs time)|
|infinite plane segment||The infinite lifeline all the blueto green eyecolored mes. Or two attributes, one limited and oneunlimited;all the blue to green eyed and happy or sad mes. Or aphysical 2Dobject with length and infinite width. All real numbers from7 to88, colored any shade of white, black, or gray.|
|limited plane segment||A square or circle, or weirdshape. Thelifepath of all the mes with eye color range of blue to green, extendedfrom monday to thursday. All real numbers from to 88, coloredredto blue. A graph of distance vs time for a limited durationcovering a limited span of possible distance.|
|1D; full line||The same as a line segement, exceptextended toany extreme. All the black and white shades (deep deep black,black, gray, white, very bright white, etc), or people more or lessintelligent than me (assuming no maximum to intelligence). Orevery real number. Or, a 1D object with infinite length.|
|ray||A ray is a stretch from a singlepoint out toinfinity. This is basically one half of a line. Above thislevel, there are far too many higher dimensioned rays to botherspecifically mentioning, such as a plane-ray (a plane, extended only inone direction to fill half of 3D space), a cube-ray into the fourthspacial dimension, and so on.|
|line segment||A timeline: My life from monday atdawn tothursday 3:47pm. Or, a stretch of one attribute: all theexactmes that have any shade of hair from blonde to black, or thehyperdimensional self who actually feels being all those colors atonce. or musical vs nonmusical Socrates. Or all therealnumbers (each a point) from 7 to 80, etc.|
|finite number of points (integer)||A few people, objects, etc.|
|point||one soul (person), or one feeling oridea, or one state ofconsciousness, or one object, and so on, of having an infinite, preciseset of attributes (human, happy, tall, buddhist; and so on for infiniteattributes)|
Aristotlesaid the wise man knows all as far as possible, but nothing inparticular. He talks much about classes and attributes, breaks genusesdown into subcategories and individuals with precisefeatures. Wehave similary shown a way to break down all life and all classes downto the precise individual or object. It may seem a little oddthat something so simple and basic as a point has infinite attributes,but consider that's what a point is, a dot somewhere in vastspace-time, than needs a series of coordinats to locate it, such as apoint on a large map of many different places, or in space to locate anexact, specific planet in the galaxy. Our point has not just2 orthree spacial attributes, but infinite, ending up at location thatwould take infinite data to describe it.
We can note quickly that all of algebra can be applied to thisinfinitely dimensioned graph, the way that 2D equations can be graphedon an x-y axis, or 3D equations on a 3D graph. If we have twoattributes (height and width, or time and distance, or musical vsnonmusical socrates over time), then our 2D algebraic equations graphonto our 2D plane, showing a single path a soul might take through thisother attribute (eye color slowly changing over the course of my life),etc. And while these paths can be exact and mathematical, ourlife 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 ofintersections: a line in space intersecting a plane at one exact point,a circle within a plane, a cirlce intersecting a plan at a linesegment, etc. Applying this to consciousness, it meansanothersoul and I could intersect at the exact same feeling, except goingdifferent directions. I might be a man living the lifepath hethinks he's living, while another man occupying the exact same mentalstate might also think he's living my lifepath, but be living adifferent one (perhaps he's about to wake up from a dream).
We can consider probability. Let us freeze a singlemoment. What are the chances I am exactly neutral? They'reinfinitesimal(if we understand that 0 is a point on a line among a whole realm ofinfinite other joy/pain values). But is this the same asbeingzero? This is tricky. Even smaller, what if weselect onesoul in all of infinity to win a lottery? If all soulseverywherethink, alright, this isn't going to be me, but of course one personwill indeed be wrong. Winning this lottery would beinfathomablyastounding. No one could ever believe it. Yet itwouldhappen. Hence we give a very real meaning to a theoreticalnumberlike chances of one in all infinity (whether a small or largeinfinity). This is the fraction of myself in all of vast(Symmetric) Being.
One final major wrench we'll throw into this entire system of graphingbeing is the consideration that perhaps there are actually infiniteexact versions of me, or an object. That since nothigness canbreak apart into infinite life, then surely some other corner ofnothingness has done the exact same thing, and another, etc. Soif this is the case, and there are infinite exact versions of merunning around, then we're actually adding one more dimension on top ofevery 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 rulethat joy is rape, and created a large system to enlarge our mind's eyeof all the being created from total opposition and how it self-relates,although, we have only barely discussed this system in light ofopposition, that is, we have not even considered how our perfectun-self fits into this huge picture, the one thing (a perfect inverse)which has created it all to begin with. It's been easy toignore, just as it's a hard thing to fathom in the first place, but wewill discuss how this core idea relates to our graphs eventually,casting a better light on everything the way our theme itself casts anew light on life, and have much more to discuss as well,sincethere's always infinite more to explore and discuss in regards toscience and math, and indeed, everything else.