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This is an old revision of this page, as edited by 211.28.185.1 (talk) at 05:30, 25 February 2005. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

20/9/2004: Please don't delete too much of it... i have never laughed so heartily at a wikipedia article :P

See Talk:Time Cube/Delete for a past discussion on whether this article should have been deleted.

All the anti-Cubic arguments in the "Time Cube" article are actually wrong and can be easily refuted. However, rather than correct the article myself, I will simply invite any free thinkers who are interested in learning the Truth to debate Time Cube on the Time Cube forum. No closed-minded Academian pedants, please.

UPDATE: The forum is out of commission. However I may discuss Time Cube on user talk pages, like I did with Andrewa.

UPDATE: I'm now editing the article.

Archived debate: Andrewa vs. TIME CUBE

Editing dispute: Section removed

Four cornered?

Has this idiot not noticed that cubes are not 4-cornered, but rather have 8 vertices? Also 6 faces, and 3 faces meeting at each vertex. There's almost nothing fourish about a cube! --Jerzy(t) 19:57, 2004 Jun 20 (UTC)

Criticism of this was the subject of the section whose removal I questioned above. Perhaps some version of it should be restored after all. Bryan 21:09, 20 Jun 2004 (UTC)

It's quite simple, Jerzy. The cube ROTATES about an axis passing through the centre of one face and the centre of an opposite face. Just like in a 4-corner room, the Cube's corners are the VERTICAL EDGES; more specifically, the four edges that are parallel to the rotational axis. And the faces can then be categorised into a group of 2 and group of 4; the group of 2 includes the ones to which the axis is normal (these may be interchangeably referred to as the Top and Bottom) and the other 4 are like the 4 walls of a room; the EDGES (not vertices) joining them are the 4 CORNERS.

Yes, the Cube is not inherently "fourish"; the number four is derived from the ROTATING cube that I have described. Also note that the rotating cube is dilated; as the rotational speed slows down and approaches zero, the magnitude of dilation also approaches zero. Now may I ask whom you are calling an "idiot"? I'd say if you cannot understand these simple concepts, then maybe YOU are an idiot.

I apologize for my reckless user of the wildly inappropriate term "idiot", which denotes lack of raw mental power. "Maniac" is closer to the case, as suggested by imagining that rooms are four cornered from their cubical status rather than from being what even idiots call "rectangular" or "square-cornered", and imagining that rotation affects corner count. --Jerzy(t) 16:22, 2004 Jul 4 (UTC)

Jerzy, the Cube-like room is merely an ANALOGY. The 4 corners of a room are the vertical edges, right? Now if we have a non-rotating cube, it is not possible to non-arbitrarily designate four of its twelve edges as corners. (The corners are the VERTICAL EDGES.) But if the Cube is rotating about an axis that passes through the centre of one face and the centre of the opposite face, then we can say that the 4 edges parallel to the rotational axis are the 4 CORNERS, and again note that I have defined CORNERS as VERTICAL EDGES (more specifically, edges parallel to the rotational axis).

I think what you meant by ""rectangular" or "square-cornered"" is that a room is as a rectangle projected along the vertical axis. Well, this is perfectly compliant with what I've described; project a rotating square along an axis that passes through its centre and is normal (perpendicular) to it, and you will get a rotating dilated Cube (it will only be undilated if you projected it along a distance equal to the square's side length).

Did I say that rotation affects corner count? No I did not, so maybe you should read my posts more carefully in future. What I did say was that just as the direction of gravity defines which of the 6 faces of a room are the 4 Walls, the orientation of the Cube's rotational axis defines the orientation of its 4 corners; and I also mentioned that rotation causes dilation along the rotational axis.

The validity of what you are trying to get across is not mirrored in the comprehencability of your argument. A simplification would indicate perspective and dimensionality. The two-dimensional representation is the only measured state for this quadrant theory, and the two-dimensional representation mirrors the three-dimensional representation only when the line of perspective is directly perpendicular to the face of the cube. At any time other than the precise time that the three and two dimensional representations are the same, the quadrant theory no longer applies. Flying Hamster 07:03, 28 Oct 2004 (UTC)

Actually I don't quite comprehend what you're saying above. By "perspective" are you referring to the perpendicular axis along which the 4-corner square is projected to form the 4-corner Cube? I can't see why the axis' alignment would shift such that it'd no longer be perpendicular.

One's saying that only viewing it face on do the top and bottom disappear. lysdexia 21:43, 10 Nov 2004 (UTC)

Funny

After reading it for the second time, I suddenly found Gene Ray's website to be the funniest thing I'd ever seen. Something in my mind clicked over from scepticism to overwhelming amusement at its bizarreness. Hence I am now compromised to the point where the only words of criticism I can muster are Evil Ass Educators Suppress Time Cube, and dumb ass students condone such evil. Cubeless institutions are spreaders of evil, and students lack mentality to challenge it. And ain't it the truth. -- Tim Starling 07:50, Jun 29, 2004 (UTC)

Help

Hi. I was wondering if some of you could help in dealing with a similar issue to this one. As I'm kind of new here, I don't exactly know the best way to deal with this. Someone named togo has been maintaining a rather nonsense and POV article called Holomovement. Although the subject matter is something that is actually quite worthy of attention, the article itself is absolutely unsatisfactory. I wrote a new article on the subject, and I think the best thing to do is to redirect to it.

Thanks,

Floorsheim 23:30, 16 Aug 2004 (UTC)

Anon,

Here are the reasons I've made the changes to the article that I have:

• I disagree with your changes to the first paragraph. Adding the phrase "Critics of the theory claim" is inaccurate. It is a fact that no one has been able to make a clear statement of what Mr. Ray's ideas have to do with time. If you can do this, do so, and I'll support changing the sentence. Also, it currently is a fact that Mr. Ray's theory makes no testable hypotheses or predictions. Again, if you can supply some, do so, and I'll agree to changing the sentence.

Dr Ray says that "Time is Cubic, not Linear". My interpretation of this is that by "Cubic", he means 3D. So Time Cube dictates that Time has 3-dimensions, which contradicts 1-dimensional linear-time models.

It is equally unclear (to me at least) what it would mean for time to have 3-dimensions. It is also unclear whether or not such a thing is what Ray means by the statement "Time is Cubic, not Linear" although that may be your interpretation. Floorsheim 06:40, 13 Sep 2004 (UTC)

I think it is clear; "linear" is a line, which is 1D, and "cubic" is a cube, which is 3D. I have studied Time Cube a fair bit, and am quite confident that Cubic Time is 3D.

Time Cube dictates that everything is cyclical, any given entity is either composed of opposites or has an opposite, everything is finite and the forms of higher living beings are related to 4 (eg. higher animals have 4 limbs which tend to have 4 fingers/toes each, golden rectangle can be approximated by a rectangle composed entirely of 4-corner squares with increasing sizes, etc.) I think that it is scientifically falsifiable—if something were observed that didn't conform to it, then that would disprove it.

How about a non-rotating sphere? How about a circle? How about a deer antler? How about the word "among"? Presumably yourself or Mr. Ray could come up with some obscure way in which these things could be related to the number four. But someone else could come up with another no less obscure way in which they were related to the number three or two or six hundred and two. The fact that, for any two things, there is always some means of finding a relationship between them is what makes the theory unfalsifiable as it amounts to doing exactly that between everything and the number four. Floorsheim 06:40, 13 Sep 2004 (UTC)

I would have to do more study into antlers to determine the principles governing their form. Do you know of any existing research in this regard? The equator is a circle formed by rotation; it may be harmonically divided into 4 quadrants and bounded by a 4-corner square. Non-rotating spheres would not often naturally occur; AFAIK, the vast majority of planets do rotate and are dilated. Manmade spheres and words are but fictitious ephemeral phenomena, which may be disregarded on the basis of their triviality.

If you have an alternative theory relating to "number three or two or six hundred and two" I would like to hear it, in the interest of free thought and rationality.

• "More specifically, these continua tend to be cycles, which the 4 classes divide into quarters or quadrants." The meaning of this sentence is unclear. I'm reverting the paragraph for now.

Consider one period of a cycle; you can divide that into 4 equal quarters (eg. sunup-midday, midday-sundown, sundown-midnight, midnight-sunup). If the cycle involves going around in a circle, then you can accomplish the 4-quarter division by dividing the circle into 4 quadrants.

You could also divide them into five quadrants, seven quadrants, or a billion sections. The very fact that they are continuous means that you can divide them into however many sections you want. Also, I don't know what you mean when you say that the continua tend to be in cycles. Floorsheim 06:40, 13 Sep 2004 (UTC)

See the graphical explanation for the harmonicity of 4, which invalidates the other divisions. Once you divide it into the harmonic 4-quadrants, that's all there is; further divisions must occur within the existing quadrants. If you walk around in a circle, that's a cyclical continuum. The continuum is a cycle.

• "(family time ages of metamorphic human)" The meaning of this is unclear. I'm removing it.

That is terminology Dr Ray uses to refer to the baby-child-parent-grandparent life-cycle.

Maybe so but the meaning is still unclear. Floorsheim 06:40, 13 Sep 2004 (UTC)

Metamorphic => metamorphic progression through the life stages. Family => parents having babies. Ages => the age of the human. Human => vertical Word-ape. Time => Cubic.

• "Midday, Sundown, Midnight and Sunup" These are times of the day. If you want to use these words to refer to corners of the earth, you need to establish the connection. I've made an effort to do this.

You're right, I made a mistake there. Consider a single point in time; sunup, midday, sundown, midnight can be used to define 4 corners in space. Then in 1 rotation, each of those corners rotates through the initial positions of the other 3 before returning to its own initial position. That's 4 Time corners for each of the 4 space corners, which sums to 16 total spacetime configurations. A graphical explanation of this is here.

• Made numerous changes to the 4-day section. Mostly to establish more clarity about the four corners of the earth but also to present some ambiguities.

At the poles, the corners cancel out, so near the poles, they are not well defined. However, you can extrapolate them from the more equatorial regions where they are well defined.

• Assuming you are Mr. Ray, you ought to know whether you claim that the four seasons are occurring simultaneously at different points on the earth. Based on your edit, I'm guessing you don't. Therefore, I'm removing the paragraph.

No I'm not Gene Ray, and I was merely attempting to neutralise the POV present in what someone else wrote.

In that case, let's leave the paragraph out for now until someone can bring in some evidence as to whether or not this is one of Ray's claims. Floorsheim 06:40, 13 Sep 2004 (UTC)

OK.

• "However, it is arguable that the transitions between life stages are somewhat indefinite, and that the precise 4-corner division functions as a useful approximation of this." It is unclear what this means. I'm removing it for now.

Well, for instance, although populations do not form a perfect bell-curve, the bell-curve is still a useful approximation. Likewise, although people's life-cycles aren't perfectly clockwork and are subject to much variation, the 4-corner division still functions as a useful approximation.

If you can supply some evidence that Ray sees his four corner view of a person's life as only an approximation, we'll rework the paragraph. Until then, let's leave it as is. Floorsheim 06:40, 13 Sep 2004 (UTC)

He stated that it's an approximation in the MIT Time Cube debate. A panel member asked him where great-grandparents fit into the life-cycle, and he said that there are variations from person to person (great-grandparent being one variation) but it averages out to four.

• Added context to the quote in the "Words are evil" paragraph.

• Supplied some pertinent additional information concerning the online petition.

• Made copyedits for clarity and succinctness to "Problems with the Time Cube symbolism"

• If the Earth were to stop rotating, although there would be many other immense changes would take place, the Earth's surface would not become spherical. This seems to invalidate paragraph #3, so I've removed the entire paragraph.

Due to gravity, non-rotating bodies tend to collapse into an approximate sphere. This may not be so much the case for a small rocky planet like Earth, but it certainly is for large gas planets and stars etc. Please explain the exact basis for your prediction above. Time Cube applies to all planets/stars/galaxies, not just Earth. I think the paragraph in question needs to be put back in the article.

If the statement it is to apply to all planets, it would have to apply to Earth as well. Floorsheim 06:40, 13 Sep 2004 (UTC)

It's an approximation. If earth stopped rotating, I'd expect some stress would occur on the crust, as gravity would be pushing it towards a spherical form. These forces might be counteracted in the case of the Earth, but not so for other planets. On average, non-rotating planets would tend to become a sphere. What is the exact basis for your initial prediction?

• Removed the paragraph about algebraic cubes. I don't see how it's relevant.

It is somewhat relevant since people do sometimes bring up the issue. It's not essential though.

–Floorsheim 05:41, 6 Sep 2004 (UTC)

I'll be happy to address these issues. However, it will have to wait until this weekend. –Floorsheim 11:47, 9 Sep 2004 (UTC)

I'm making a few changes as of now to correct some mistakes I made in assuming the Anon who made the 11:04, 4 Sep 2004 edit was Gene Ray. Also, I disagree with the use of this sentence "It therefore falls into the category of speculative belief with little relation to physics or science in general." Certainly there are some who would define the categories "speculative beliefs"and "beliefs with little relation to science in general" as not precisely overlapping with "beliefs that are not scientifically falsifiable." I'm reworking the sentence. –Floorsheim 06:40, 13 Sep 2004 (UTC)

This article is, in my opinion, (and please hear me out before you stop reading when I complete this sentence) one of the most important in the Misplaced Pages. It is an example of a running controversy that demonstrates how Wikipedians actually apply the policies of this project. One camp hates the mere presence of the article as something that pollutes Misplaced Pages, while another camp fervently believes that the information given is genuinely useful and true. So I've been following the edits to watch how Neutral point of view is being applied: how much do editors assume that their opinion is the only one that should be presented; how often do editors use loaded terms (and was it intentional?); and how are disputes conducted on this Talk page? Because the page is not about some violent international conflict or suchlike, it's free of the worst forms of arrogance, and allows me to appreciate the dynamics of the edit history without worrying about who gets shot in the end. Still, however, it's interesting to note what goes on here.

Cheers, One-dimensional Tangent 01:05, 30 Oct 2004 (UTC) (May delight find you in the strangest places.)

it's poetry

I don't where to put this in the actual article, but has anyone else noticed how poetic his entire site is? You could turn down the lights and read it off in a beat fashion, and it'd work perfectly.

A 'Big Bang' for Academia.
A 1 day Earth = 1 leg horse.
A 4 day Earth = 4 leg horse.
4 quadrants resemble circle,
but doesn't constitute circle.
Earth more Cubic than orb.

disputed

Ray also offers $10,000 to any academic institution or professor who disproves Time Cube, and $1,000 to anybody else who can disprove Time Cube.

I'm interested in what disproofs have been offered so far. A long time ago I wrote and emailed a paragraph easily disproving the main one or two pages, but got no reply. Since I don't feel like going onto the page again, I'll work within these articles. (Dammit, I'm the one claiming to disprove all religious and scientific ideas, and to be above God... I've even reinvented the calendar, as well as all other basic ideas and tools, using an essential number based on time and geometry, but not 4. But these hundreds of plans I save for websites, should I ever get them up, and after I put up a user page on Misplaced Pages outlining my anomalous history.)

Gene Ray explains the 4/16 Rotation Principle, an important element of Time Cube, as follows: "If Earth stood still, it would have mid-day, mid-night, sun-up and sun-down as 4 corners. Each rotation of earth has 4 mid-days, 4 mid-nights, 4 sun-ups and 4 sun-downs. The sixteen (16) space times demonstrates cube proof of 4 full days simultaneously on earth within one (1) rotation. The academia created 1 day greenwich time is bastardly queer and dooms future youth and nature to a hell."

His material is very easy to understand if you're not dumb, and easy to disprove if you're not mute. The problem here is that he stops on 4, rather than other special numbers like 2, 6, 8, or 12. He first points out the opposites of faces, divided here by a quality based on solar illumination. That makes two. But then he includes the two lesser halves, which are mixes of the two, and fails to consider that the proscribed mixing of races elsewhere in the explanation would be equivalent to them. At sunup and sundown, the Earth is at an intermediate illumination; these places are also subordinate to the faces determined by illumination. So his theory should realise that Indians and Asians shouldn't exist.

A corollary mistake is using an arbitrary, ad hoc model of a cycle for the divisions of races which developed on the surface beginning on one face, the region shared by the borders of all four hemispheres, with the cradle of humankind on one end and the cradle of civilisation on the other. The number of races then have more to do with a combination of the tiling of the plane, along with its kissing number, and the primary set of races truncated at their intermixing. So one arrives at three proper races, rather than six. However, because the racial divisions correlate with solar illumination, the three show the blending of the two Earth faces established above: light (European), dark (African), and blend (Asian). The "Indian race" he uses is not really a race; because we've already established three sheer, right races, the other groups can only be subraces or superraces, the latter being a superposition of all three qualities. The Indians would then be grouped in a superrace, the IndoEuroIberians, including Scythians, Kurgans, Kurds, Semites, and Mediterraneans. Diagrammatically, the three races form a triangle over the surface of the Earth, with the superrace at its centre. Because the superrace is not counted as a race, and the surface is disconnected with the rotational cycle, there are only three races.

A typical Ray quotation is "Time is CUBIC, not linear as stupid educators teach."

He says "infinite days is stupidity", implying that it is correct to divide Earth into precisely four classes of location, and that a continuum of locations is incorrect.

Not having a mathematical background, Ray equivocates cubic for cubical. He also equivocates motion for time: Time is independent of the Earth's spinning, or of any other cycle; he describes only a concept of periods crossed with structures as the basis for his theory. Because his four-corner model is completely arbitrary and ad hoc, suitable only for describing the differences between places on a round object only after freezing time, so that these places are established by pointing out where the sun is overhead for some such example, it doesn't at all matter to other places/"corners" on the Earth where the four corners are in other rotated examples. The examples do not constitute days but shifted intervals in days, which don't touch the meaning of time itself.

A person's age is not on a linear continuum; instead, when a person advances to the next corner of their lifetime, their old corner dies. This forms a 4-stage continuum, like a circle divided into 4 quadrants.

• The four corners/stages of a person's lifetime are baby, child, parent, and grandparent
• The four corners of a person's head are the face, two ears, and back of the head
• The four corners of Earth are the following: the places where days start at midnight, the places where days start at sunrise, the places where days start at noon, and the places where days start at sunset. Mr. Ray calls these corners Midnight, Sunup, Midday and Sundown, respectively. (more on this below)
• The four corners of the day are midnight, 6 AM, noon, and 6 PM
• The four corners of the year are the two equinoxes and two solstices

But the human life doesn't visibly loop into a circle; it's a line from start to end. Because of this, the number of classes should be odd: line (1) -> start, to<->middle, end (3) -> 1st, 2nd, 3rd, 4th, 5th (5) -> etc. Then the stages of a lifetime are youth, adult, and elder; or baby, youth, adult, elder, and crone.

A head isn't regular like a planet is; it's an outgrowth biased (anisotropic) forward. So the face isn't the same size as the back, which melds with the top. (Yes, there is a top.) Because the animal head started from a four-legged creature, the face would point slightly down. This being the first facet in terms of prominence, the second facet would be the top of the head. The back would not be a facet because there was no evolutionary pressure for that part to grow something there; therefore, the left and right back halves, including the ears, would be two more facets. So those form four facets, but unlike Ray's model, they are arranged as a distorted tetrahedron with facet pairs perpendicular rather than coequatorial as conformal belt.

And of cyclical divisions, in my reformulation of measures I don't use corners (Why should I? A ring is not a square.) so my division isn't four, but something much better.

Gene Ray has stated in the January 2002 MIT Time Cube Debate that the concept that -1 times -1 equals +1 is stupid and evil, because it is like saying that "A South American times a South American equals a North American." He jokingly added that -1 * -1 should actually equal "A South American".

Actually this is true! A South American times a South American does equal a North American. "South" to a southener is "north", as Australians consider Americans to be down under.

As for what one should call the object, try timecarton. :P

lysdexia 21:43, 10 Nov 2004 (UTC)

Hmm, yeah

Gene Ray is probably the most talented and disciplined performance artist I've ever seen. Even Misplaced Pages article writers don't even seem to get that this is one big practical joke. --I am not good at running 11:17, 6 Jan 2005 (UTC)

If it is a joke, that would be news to me. I am quite convinced that Gene is for real; more importantly, even if he doesn't really believe in Time Cube, I know that I can support the Cubic principles using evidence and reasoning, and not mere citations of Dr Ray's scriptures that rely on the assumption of his authority. The article contains some of this supporting body of evidence/reasoning; you will notice, at least, that all anti-Cubic arguments contained therein are accompanied by a refutation. If you have good reasons to believe that Dr Ray is joking, please state them, or add them to the article.

On a more serious level, I also used to believe that the Time Cube phenomenon was an arch riff on internet conspiracy theorists, but have since come around to the belief that Gene Ray genuinely is a bit odd, albeit in a harmless way which is hard to dislike. Whereas most internet cranks are genuinely unpleasant people, or obviously profiteers, Ray seems closer to the inspired madness of Spike Milligan or Stanley Green, the 'protein man' , than the face-on-mars/moon hoax people. I wish him well. -Ashley Pomeroy 11:41, 21 Jan 2005 (UTC)

Mathematics?

I am puzzled by the mathematical claims. He claims that ${\displaystyle -1\times -1=1}$ is incorrect. Such a question cannot really be resolved without understanding what we mean by 1 and ${\displaystyle -1}$. Let me state my assumptions about this, and derive the result from those assumptions, and hopefully someone can point out which of the initial assumptions are flawed.

To have any concept any concept of "multiplication" as well as "negative numbers" we should probably be considering a Ring with Unity (multiplicative identity). In that sense we define 1 as the unique element of the ring ${\displaystyle R}$ such that

${\displaystyle 1\times a=a\times 1=a}$, for all ${\displaystyle a\in R}$

And then -1 is simply notation for the additive inverse of 1, that is the unique element of the ring such that

${\displaystyle (-1)+1=1+(-1)=0}$

Given those definitions and the ring property that ${\displaystyle a\times 0=0\times a=0}$ for all ${\displaystyle a\in R}$ we can write:

${\displaystyle 0=(-1)\times 0=(-1)\times (1+(-1))=(-1)\times 1+(-1)\times (-1)=(-1)+(-1)\times (-1)}$

thus ${\displaystyle (-1)\times (-1)}$ is the inverse of (-1), which is 1 (by uniqueness of additive inverses).

Now the uniqueness of identities and (additive) inverses, and the ring property stated are easily proved from ring (or group) axioms, and I can reproduce those with ease if required, but I don't think that would be necessary. The only really open assumptions I can see is the assumption that we have a ring and thus distributivity, and the very concepts of what we mean by the symbols 1 and -1 anyway.

Any discussion would be appreciated. 65.95.167.120 07:21, 15 Feb 2005 (UTC)

See -1 * -1 = +1 is Stupid and Evil; negative and positive are to be considered equal opposites, voiding the accepted Academic positive-bias and giving rise to the following equation:

-1 * -1 = +1 * +1 = -1 * +1 = ±1

Therefore:

1*a = a*1 = ±a

The assumption of the additive inverse, however, is compliant with the principle of opposites: it makes sense that when you add the two equal opposites together, they cancel out to zero.

0 = (-1)*0 = (-1)*(1+(-1)) Split = (-1)*1 + (-1)*(-1) = ±1 + ±1

The result is -2, 0, 2, which includes the initial zero and averages thereto, but also reflects the fact that you have Split apart the zero into its polarised components, like splitting apart a photon into a positive and a negative particle.

I'm going to have to ask you what you mean by various concepts like "*" and "=" because your usage potentially differs greatly from most standard defintions.

Let's assume that

1*a = a*1 = {-a,+a}

as you've stated. Now what do you mean by multiplication? We can use generalised mathematics, but you seem to want to stick with integers, so we'll stay there. Most people commonly mean

a + a = 2*a

a + a + a = 3*a

and so on. If we assume that you also mean this by "*" then we can write

a + a = 2*a = (1 + 1)*a = 1*a + 1*a = {-a,+a} + {-a,+a}

I'm attempting to follow how you add these sets of numbers. Can we say

{-a,+a} + {-a,+a} = {(-a) + (-a), (-a) + a, a + (-a),a + a} = {(-a) + (-a), 0, a + a}

or is that not what you mean?

That's it; by including the negative and zero results with the positive one, it reflects the totality of the real-life situation, rather than the 1-corner self-perspective. If you pick 2 apples, you get +2, but the tree from which you picked them gets -2, and it averages to zero overall.

Okay, I just wanted to be sure, as a set is a different object than a number, and thus addition of sets is not (yet) a well defined operation. While we're making sure I understand your definitions, how does multiplication of sets work? For example, what is {-a, 0, a}*{b,c}?

134.117.137.149 17:06, 23 Feb 2005 (UTC)

I am unsure of that, as {b,c} doesn't necessarily represent a set resulting from a single-number operation, such as {-a, 0, a} which represents a one-way transaction of a. If it were {-a, 0, a} * {-b, 0, b}, I think it could be reduced to a * b and then expanded out again to {-a*b, 0, a*b}.

You can probably figure most of this out yourself, as I am basing it not on anything particularly complex or esoteric, but merely on the simple Cubic principle of equal opposites, as applied to the positive and negative signs. It is required that they be equal opposites, which precludes any bias towards one or the other.

Either way, I am now struggling to understand what you mean by "=". Usually people mean the objects are identical. Mathematically (in an algebraic sense as this is) we mean that the objects have the same algebraic properties. Neither of these concepts of "=" accepts

a + a = {-a,+a} + {-a,+a}

as a valid statement, so presumably either you mean something different by "*", or by "=".

I could suggest that you have introduced a new symbol "Split=" that relates objects differently than the "=" you use to equate numbers. Hopefully you could explain when two objects are "Split=".

65.95.167.120 00:23, 17 Feb 2005 (UTC)

No I did not intend "split" as a symbol, rather it was to denote the point at which the zero is split into positive and negative components.

So if it is not a seperate symbol, we are back to the issue of what you mean by "=", because, as I said, it does not agree with either the common use definition, nor the strict mathematical definition. What I mean is, how do I know when two sets are "="? For example, given a set {a,b} and a set {c,d,e}, what must be true before I can say {a,b} = {c,d,e}?

134.117.137.149 17:06, 23 Feb 2005 (UTC)

As with any other equation, to prove equality, you must manipulate the two sides until they are identical. Here we are discussing principle-opposites-compliant operations on signed numbers, so the relevant manipulations would be those I have presented, derived from the concept of negative and positive as equal opposites.

A couple other quick questions, based on what you mean by "=":

Is -1 + 2 = 1 still true?

Is 1 + 1 + 1 = 3 still true?

Based on what I have seen previously, the Academically accepted result is included within the full principle-opposites-compliant set, so I imagine that this would be the case with the equations above. The results (RHS) would be true, but only represent one of the multiple outcomes; the truth, but not the whole truth. If application of the Principle of Opposites would have any unforeseen consequences on the above equations, please explain them.

1+1+1 has multiple outcomes? Can you list for me all the possible outcomes? Are all the outomes "=" to each other? If all the outcomes are not "=" to each other then what do you mean by "1+1+1" or "1+1" for that matter? I would appreciate it if you can actually describe how this mathematics actually works it total, because you seem to be using standard symbols to mean completely different things ("=","*","+")

134.117.137.149 17:06, 23 Feb 2005 (UTC)

It works under the initial condition that negative and positive are to be treated as equal opposites. 1+1+1 could be expressed in different ways: 2*1+1, 3*1, etc. One would determine all the different expressions, then evaluate them according to the principle-opposites-compliant rules.

The multiple single-number outcomes would be collected together as a set. I think it would potentially be invalid to separate one element of the set and declare it equal to the expression from which the set was generated.

Thanks, 65.95.167.120 22:13, 17 Feb 2005 (UTC)