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Talk:Time Cube/Archive 1

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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 (e[.]g. 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 (e[.]g. 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 Wikipedia. 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 Wikipedia, 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[sic] 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 Wikipedia 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 [conformal] 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 [a] 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 Wikipedia 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?
Unfortunately I have more important things to do now, and while philosophy of mathematics was interesting and somewhat related to my work, semantic games are merely a time consuming annoyance that I can't spare time for. 65.95.160.205 02:56, 2 Apr 2005 (UTC)

 * It seems that you also can't spare time to explain the rationality supporting your mathematical beliefs, or to justify your claim that terminology misuse disproves the Time Cube principle. While this remains the case, I suggest that you also not spare the time to revert the article.

Pointless

This debate has become quite pointless. I am happy to debate foundations of mathematics and philosophy of mathematics. I am happy to consider other axiomatic bases for mathematics (I commonly do so in fact). I am not interested in playing a pointless language game where words are redefined to mean whatever is required to prove the point. If you want to play semantic wankery that's fine, but I have no interest in such things. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * This is about a superior axiomatic base. It's about basing mathematics on the true Cubic nature of the universe, rather than 1-corner singularity lies. I think the problem you have is that I am using words to describe 4-corner Cubic Truth, which contradicts the 1-corner mathematics with which you were indoctrinated. It's not about giving the words a different meaning, merely translating their accepted use from 1-corner thought to true 4-corner Cube-totality.

 * It's pretty simple: you are using commonly used words to mean different things. You have redefined *, +, -, and = to mean something different that is not compliant with the usual definition.  You have misused concepts like "equal to", "multiplied by", calculation of areas, special and general relativity, particle physics, and complex numbers.  You have abused mathematical notation using ambiguities in the average persons understanding of their meaning to find "inconsistencies" in mathematics that don't exist.  I've read some of the other discussions on time cube by others in the past - they complain of exactly the same thing: misuse and redefinition of preceusely defined technical terms to mean something different.  This seems common to all time cube supporters (unless of course there's only one of you making these arguments).  I am happy to argue mathematics, but I see little point in arguing semantics. 65.95.160.205 21:22, 30 Mar 2005 (UTC

 * I have addressed your arguments regarding use of "equal", "multiplied". You have not given any arguments supporting the following: "You have misused concepts like ... special and general relativity, particle physics, and complex numbers." In discussion with others in the past, the claim of "misuse of technical terms" has been used without substantiation, as an "ad hominem" attack. Hopefully you are not doing the same. Since we don't what "ad hominems" and other subversive rhetoric miring the article, you cannot add this claim to it unless it actually helps to explain the concepts.

 * This is just demonstrating the pointlessness of this argument. You have not "addressed" my argment rearding use of terms other than to say (paraphrasing) "no, I am using them correctly" or "I am using words to describe 4-corner Cubic Truth, which contradicts the 1-corner mathematics".  The first amounts to a block denial, which means you either are not aware of how the term is defined (please go read a formal source, or talk to other people about what it means), or you are simply being obtuse, it hardly "addresses" my concerns.  The second amounts to agreement that you have redefined the terms to mean something new that is inconsistent with the common definition.  That "addresses" the concern in as much as it admits that it is entirely true.

 * Again, see -1 * -1 = +1 is Stupid and Evil, in which standard manipulations are performed within the established system to prove its inconsistency. Since anything "inconsistent with the common definition" is, by your standards, not allowed on Wikipedia, the common definitions, being inconsistent with themselves, must not be allowed. We'd better get started deleting every article pertaining to mathematics; it will be quite a task.

 * I've explained quickly why that argument presented on that site is just a misuse of notation, exploiting common confusion about mathematical symbols. If you want a formal derivation of everything I've been talking about then by all means read Principia Mathematica which has a a completely formalised, logical, rational explanation of why imaginary numbers exist and why they are perfectly consistent.  If you can point to a website and say "until you refute this it stands", then I can point to a widely cited extremely rational book and say "until you dispute this, it stands".  Find me the flaws in the reasoning in Russell's Principia Mathematica that make imaginry numbers inconsistent and we'll talk, until then you are simply pointing to a misuse of technical notation (while at the same time claiming you don't abuse terminology or notation) as an argument, while not refuting the full rational derivation that shows that it is consistent. 65.95.160.205 02:56, 2 Apr 2005 (UTC)

 * Your stipulation is somewhat onerous, as I am required to read the whole book before I can respond. The -1 * -1 = +1 is Stupid and Evil is quite short, and so if it contains flaws in its proof then it shouldn't take too long for you to identify them. The notation is not misused; see below. I will be keeping my description on the page until I have read the text, or until you identify the flaws.

 * See below for explanation of why you yourself will need to expound on your unclear substantiation for your allegations of terminology misuse.

 * Special an general relativity and are misused on the cubicAO site you keep directing me to. Your misuse of particle physics is in your "mystical" explanations of energy moving (rotating?) one way being negative etc. The misuse of complex numbers is on the cubicAO site again, though you now, below, demonstrate your misuse again.  Imaginary numbers are every bit as real as negative numbers, and anyone who has done the rational derivation ofarithmetic, and of complex numbers, from first principles will see that to be the case.  Saying you are "not misusing the terms" when experts in the fields involved are quite sure you are is just a meaningless denial on your part.

 * Energy rotates about its linear path; that's where the frequency comes from. Without frequency: no energy. This is evidence of the omnipresent force of the 4/16 rotation.

 * If energy moves out of and away from the Sun, a loss will be experienced by the Sun. That's negative. If energy moves towards and into the Sun, a gain will be experienced. That's positive. I would have thought it self-explanatory.

 * The self-proclaimed "experts" will need to do more than make assertions if they want to be believed. They'll need to provide the actual rational arguments supporting their claims; see below.

 * As to ad hominem attacks previously: I read through the discussions an saw terms misused by the time cube supporter (you I presume, but it may not have been). You can claim that the person who argued with you used ad hominem and attacked you on errors or typos that weren't proper misuse if you like, it doesn't negate the fact that there was misuse of technical terms in those discussions.  As for my calls to that fact - they are clearly not ad hominem and claims to that effect are diversionary (another interesting debate tactic).  I am not attacking you, but attacking the fact that your argument rests on the necessity of redefining well defined technical terms.  Argument by redefinition is another debate tactic.

 * If you claim to be making a rational argument to disprove the Time Cube based on erroneous terminology use, then it is not sufficient merely for you to add to the article an assertion of such erroneous use. Rather, you must provide the complete argument, listing each of the terms misused; how they are misused; and how their misuse invalidates the Cubic principles.

 * I didn't claim to be refuting time cube with respect to erroneous terminology use, I was merley saying that it is somethign the supporters of time cube engage in. It has been documented at many points in the discussion below, on the sites you regularly direct me toward, and in previous discussions with other people (Andrewa, Kosebamse).  I've listed the terms misused above, and explained below why they are being misused.  Misuse of terms is very well documented, so I see absolutely zero reason why a statement noting that fact shouldn't appear on the page amongst the criticisms.  The statement I added is fair, doesn't claim to refute Time Cube, but merely notes the fact that terms are often misused, and that objectors to Time Cube view this as a weakness in the argument of others.  We can have a revert war if you want, but I see no reason for it not to stand.

 * What is this article about, may I ask? I notice that the title is "Time Cube". Now unless there are some microscopic words in there that my eye did not detect, the title is NOT "Characteristics of supporters of Time Cube". This means that your criticism is irrelevant if the link to the validity of the actual Time Cube principle is not made; and if such a link is made, then it must be substantiated. The only reason I can see for your adding this irrelevant content is to attempt to subvert the article with an "ad hominem" attack. Being either irrelevant or unsubstantiated, it does not belong in the article, and must therefore be removed.

 * With regard to your added passages in the math section I deleted: your argument is unsubstantiated and based on the fact that you misuse "Equal to" to mean "can be cancelled to, or anti-cancelled from". A quick check on the Wikipedia definition of Equality gives it explicitly: "In mathematics, two mathematical objects are considered equal if they are precisely the same in every way".  If the length of my table is 140cm which is, but cubic math equal to 0cm, then the length of my table is precisely 0cm in every way - which is to say it doesn't exist.  The same can be said of any object or collection of objects.  If you wish to redefine equality, by all means do so.  The the critcism comment must most definitely stay.  If you don't wish to redefine equality, then you must certainly leave the math section alone. 65.95.160.205 02:56, 2 Apr 2005 (UTC)

 * In -1 * -1 = +1 is Stupid and Evil, it is proven that when the logical consequences of the Academian definitions are followed through, 1*1=&plusmn1;. Now, a positron and electron pair (±1) equal a photon to which they annihilate (zero charge). ±1=0. It's the same as equating 2+2 and 4; 2+2=4 has different expressions on either side of the equals, but when simplified, they are found to be identical.

 * From a true Cube-perspective, your table's length is indeed zero overall, since its left-to-right length is of an opposite sign to its right-to-left length. You're only considering 1 direction in your measurement. That's a 1-corner perspective, and Time Cube proves that it's not the absolute truth you claim it to be.

 * In conclusion, read some Wittgenstein. 65.95.160.205 16:20, 31 Mar 2005 (UTC)

Discussion recorded for posterity:

This discussion has broken down into separate threads which are becoming increasingly difficult to track, and breaking up any coherence in the argument. I've attempted to gather the main points immediately below:

No matter how you phrase it there are fundamental problems here. Instead of picking at it piecemeal, I'll try and lay out some of the most glaring issues:

(1) Your founding assumption, that 1 is an incomplete object and must be expressed as {-1,+1} is woefully unjustified. As it stands you reason for declaring this necessarily true is that "things must be opposites" which fails to justify your assertion in any meaningful way.

 * How about that -1 * -1 = +1 creates mathematical contradictions and inconsistencies? The existence of imaginary numbers, for instance, is necessitated by the pro-positive-sign bias. On the webpage -1 * -1 = +1 is Stupid and Evil, it is shown that i contradicts its own definition when simple manipulations are performed on it, and can ultimately be related back to the unbiased, principle-opposites-compliant solutions.

 * Abusing notation to make an invalid operation appear valid doesn't create a contradiction or inconsistency. i contradicts it's own definition only if
 * $$\sqrt{-1}\times\sqrt{-1} = \sqrt{(-1)\times(-1)}$$
 * which, unfortunately, isn't true. You are attemtpting to use the algebraic "rule" that the product of square roots is equal to the square root of the product.  Apparently you were not taught that that is merely a convenient rule, and only applies positive numbers.  If you can show me the derivation of that rule - why it's algebraically valid - in a way that includes validity for negative numbers I'll be happy to reconsider.  You won't be able to, however, because working from first principles you'll see that the "rule" just doesn't work when both arguments are negative.  There is no contradiction there, only a misunderstanding of algebra.  There are, however, fundamental contradictions and inconsistencies based solely on your axiomatic definitions.  I suggest you deal with those rather than try create distractions.

 * (-1)1/2*(-1)1/2 = (-1)1
 * ((-1)*(-1))1/2 = ((-1)2)1/2 = (-1)1
 * What I need to see is the actual reasoning to exclude negative numbers. If it's just arbitrary, it doesn't reflect nature and is therefore not philosophically valid.

 * You are going about this completely backward. You've taken an arbitrary "rule" and are asking why (even though the reason for the "exception" is derivable from axoims) I should have an exception to the rule.  You as well say: there's a rule that 11*4 = 44, 11*6 =66 etc., so clearly 11*13 = 1313.  Why is that not true?  If you're unwilling to see that the negative numbers are "excluded" because they were never properly included in the "rule" in the first place, there's little I can do to help.

 * It's still a problem that the rule is incomplete. Occam's razor favours complete rules over ones that don't cover everything, and that require a patch (imaginary numbers) to be placed over the hole.

 * Then why is 11*13 not equal to 1313? Surely by Occam's razor the more complete rule (that you always just write the number twice when multiplying by eleven) that doesn't require special cases for numbers with multiple digits is the correct one?65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * We just use the ordinary multiplication rule. That covers everything with a single simple rule, whereas the "11*4 = 44, 11*6 =66" pattern is but a subset of it. One doesn't require special cases when using the normal multiplication rule (neglecting the sign-bias), meaning that it is not more complicated. We favour the simplest rules, and those that cover the greatest scope.

 * Good, now you can see that we just use ordinary multiplication of numbers. That covers everything with a single simple rule, whereas the $$\sqrt{a}*\sqrt{b} = \sqrt{(a*b)}$$ pattern is but a subset of it.  One doesn't require special cases when using the normal multiplication rule, meaning that it is not more complicated.  Apparently you favour the simplest rules, so you should not assume any rules about multiplying square roots, nor even necessarily assume any rules about commutivity (order of terms in multiplication) as that is the simplest possible.  You can derive rules (like the square root rule for positive integers, or commutivity) as they happen to apply the same way you can derive 11*x = xx as it happens to apply. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * When you use the normal multiplication rule to multiply $$sqrt{a}$$ and $$sqrt{b}$$, a convolution in the rule is required to account for the sign-bias. This is not required with a principle-opposites-rectified multiplication, meaning that it is favoured by Occam's Razor over the sign-biased version.
 * 11*x = xx rule is not required, because you can just perform the multiplication the normal way. But what about multiplying two square roots? How do you do that the normal way, without the rule? You can't, and so that's a lack of full scope evident in the existing multiplication. As shown on -1 * -1 = +1 is Stupid and Evil, principle-opposites-rectified multiplication doesn't require an incomplete rule, and so it is again superior to the Academic sign-biased version.
 * Actually, the square-root-product rule does apply to -1 (so no "negative exception" is even necessary), and it's a little naïve to say otherwise. Recall that every number has both a positive and a negative square root: thus $$\sqrt{1}$$ can be either +1 or -1, $$\sqrt{16}$$ can be either +4 or -4, and so forth. By convention, we usually use "square root" to mean "positive square root" (at least when referring to real numbers), but there's really no reason for this other than terminological convenience. So: $$\sqrt{-1} \times \sqrt{-1} = i \times i = -1$$. $$-1 \times -1 = 1$$ ∴ $$-1 = \sqrt{-1 \times -1}$$ (the negative root, in this case) ∴ $$\sqrt{-1} \times \sqrt{-1} = \sqrt{-1 \times -1}$$. Q.E.D. --Marnen Laibow-Koser (talk) 15:59, 30 Mar 2005 (UTC)
 * I better field this one: in mathematics the symbol $$\sqrt{x}$$ specifically refers the the positive square root (so that the function retruns a single value) that's precisely where the abuse of notation is coming in here, as your explanation shows. 65.95.160.205 21:37, 30 Mar 2005 (UTC)

 * Why does it have to return a single value? To be the inverse of y=x2, it should return two values for positive numbers. Furthermore, as the inverse of a rectified y=x2 graph (see -1 * -1 = +1 is Stupid and Evil) it would return two values for all numbers (x=0 can be seen to give two zeroes). It sounds like this requirement that it be a function is just an arbitrary single-corner rule.

 *  I better get this one as it is somethign someone else started. Yes, the symbol $$\sqrt{x}$$ is restricted to a single value, and yes that is fairly arbitrary - it si because a symbol was required to express "the postive square root of x" which is something that is said quite a lot in mathematics.  Because it is said a lot a symbol was created to express it succinctly and compactly.  There is no mysetery or obfuscation here, except that provided by the time cube supporters, who either do not know the difference or are deliberately misusing the symbol.  If you want the symbol for "all solutions to the equation y^2 - x = 0 (which will give you the positive and negative results) then you want the symbol x^{1/2}.  You will, of course, note that ((-1)^{1/2})^2 is not equal to ((-1)^2)^{1/2}.  This is pretty clear given that x^2 returns a single value but x^{1/2} returns two values, so order of exponenatiation in this sense is important.  This just goes down as one more misuse of technical terms.

 * But as is clearly evident from reading -1 * -1 = +1 is Stupid and Evil, the positive-number-only x^2 function is self-contradictory. The true version includes both negative and positive numbers; this invalidates your argument. It looks like it's actually going down as an Academian misuse of rationality.

 * I am not going to try and have an argument on axiomatic math piecemeal, as it's going to pointless and frustrating. There is a perfectly good solid explanation of how to derive all of arithmetic from exceedingly simple set theoretic axioms in Principia Mathematica by Bertrand Russell and Alfred North Whitehead.  If you can find errors, contradictions, or inconsistencies in that I'll be interested to hear them.  If you can't I think we can safely say that, assuming the axioms Russell uses (which are fairly safe), mathematics is solid. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * Above I mention Occam's Razor; it is quite possible to have a system that is solid, but excessively convoluted. For instance, one where a sign-bias is patched by making rules that only apply in certain circumstances, and nonexistent imaginary numbers intended for use in lieu of the real numbers that were excluded by the sign-bias.

 * If you wish to use Occam's razor to define mathematics then you will end up with the system you're using - which is to say a system where there are no numbers other than zero, every calculation is necessarily equal to zero, and every mathematical statement is necessarily true (and also necessarily false). Congratulations, you've created the simplest possible arithmetic system.  It doesn't reflect reality in any useful way, nor tell us anything interesting.  It is worth noting that we are not "constructing rules that need to be patched but merely construting rules.  The domain on which the rule applies is at issue, but you may as well question why the rule 1/x doesn't work/requires patching for the case x=0.  It's just semantic sillyness and doesn't show anything.65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * It does reflect reality, because matter and anti-matter cancel to zero, negative and positive cancel to zero, and left-moving energy cancels right-moving energy to zero. Everything reduces back to zero, but likewise, zero expands out to opposites. We are created between the opposites, and our single-corner perspective exists in the context of full 4-corner, 2-opposite Cubic geometry.

 * I have never witnessed zero expanding to opposites, nor have I witnessed "sign" being the only form of opposites. Opposites take many forms. In multiplication opposites take the form x and 1/x, in the Symmetric group opposites are different again, with matrices opposties are different yet again.  You fundamental misunderstanding here seems t be assuming that the symbol "-" means "opposite".  I challegence you to justify that claim, and show that that prepending "-" will always produce the opposite of an object.

 * When a photon splits to positive and negative charges, that's zero splitting/expanding to opposites. As shown on -1 * -1 = +1 is Stupid and Evil, true sign-neutral multiplication would give -x, -1/x, 1/x, x, which means that the -/+ opposites are also evident with multiplication.

 * Besides, to say that "everything cancels to zero" is very different from "everything is equal to zero". The mathematics says the latter, you are arguing the former  Unless you wish to redefine "equal to" to mean something different (and you are wont to redefine terms to whatever is required to justify your assumptions) your explanation is no justification at all, but merely obfuscation.  If I measure the width of my table it is, by cubic math, equal to zero.  That would mean that it should not be visible.  Yet it is.

 * You measure width of one metre left to right. Opposite to that is one metre right to left. +1 -1 = 0 overall. You only get a result of 1 metre from a 1-corner perspective taking into account only the left-to-right direction.

 * There is a glass on my table - a total of one. By cubic math that is equal to zero glasses, and hence is not there.  The rest of the universe was never invoked nor included in my calculations, so you cannot cancel with any object outside the calculation - the only objects are: my table, and the glass on it. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * You count the glass -- "counted" gets +1, "uncounted" gets -1. That cancels to zero. If you are considering only the table's 1-corner perspective, then it's +1. But if you want to include the full Cubic totality, then the 4-corner 2-opposite rotation will cancel out to zero.

 * To my knowledge, no-one has ever required an imaginary number to represent 1/0. But they have required them to represent the square root of -1. That represents a hole in the system, for which imaginary numbers were invented as a patch. They are seen as imaginary from the 1-corner perspective, because limiting your perception to 1-corner precludes recognition of the full 4-corner reality.

 * Given that there is no contradiction in "one-corner" arithmetic, I'll ask you again for justification of your assertion that 1 is an incomplete object and must be expressed as {-1,+1}. 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * You have argued that the contradiction is not present when a rule is imposed to exclude negative numbers from the operation. However, as above, this rule must be justified with a non-arbitrary reason. If it's just to patch the hole, then Occam's razor would dictate that a simpler theory, one without a hole in the first place, would be favourable.

 * The reason is derivable from basic axioms. It's long tedious and complicated for me to render the whole thing here.  As I said, read Principia Mathematica as it provides the derivation if you want it - it will be quite long to build it up from initial axioms. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * So, you can rebuild it from the axiom of the Principle of Opposites. That should make it simpler, since it won't require rules limited by a sign-bias and imaginary numbers to cover up the hole.

 * Yes, and what you get is an incosistent system in which there is only one number, 0 (note the contradiction there!) and every mathematical statement can both be proved true, or proved false. Godel showed that you can't prove a system to be consistent within itself.  You can, however, prove a system to be inconsistent from within itself.  I've done that you for your system.  In an inconsistent system any statement in the system can be proved to be both false and true.  That makes it, for logical purposes, rather useless.  You're welcome to use it anyway though - it certainly is simple. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * Exactly, it can be considered either false or true. So when the religious zealots consider it false and word-murder their children and destroy nature, the extinction of humanity results; with the Cubelessness destroyed, Cubic harmony is restored. And if we consider it true, we can extinguish the Cubelessness ourselves and create our own Cubic harmony. Either way, Cubic harmony eventuates. The false-true dichotomy represents an ultimate, 4-corner Cubic truth.

 * No, on the contrary the zealoutous time cube supporters weird the language with verbing and the incomprehension of humanity results. If false it true and true is false, then surely truth is beauty, and the tree in the forest makes no sound. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * False is true and true is false from a false perspective. True is true and false is false from a true perspective. The tree in the forest makes a sound, because when it falls it causes sound waves to travel through the air.

 * Furthermore, in the philosophical sense, mathematics should reflect reality. Let's consider positive and negative charges. Create a four-by-four grid of positrons, we get 4*4=16. Create a four-square grid of electrons, we get -4*-4=-16 -- NOT -4*-4=16, as the Academian mathematics would dictate.

 * A four-byfour grid of electrons will give you a total charge of 4 (rows of electrons) * 4 (columns of electrons) * -1 electron volts (charge per electron) = -16 electron volts. Cursory unit analysis will show that what you are doing simply makes no sense.  If you want a physical description of multiplying by a negative how about this:

 * -1 is the number of things I would have if I started with 1 and took away 2. To multiply -1 by -1 I can view it as stating with 1 lot of -1 then taking away 2 lots of -1, so that's -1 less (-1 + -1) or -1 - (-2) = 1.

 * Row: 4 * -1 positron (charge per electron)
 * Column: 4 * -1 positron
 * Grid: (4 * -1)*(4 * -1) = -16 (not the academic +16; an academic inconsistency is evident)

 * Right, so you do mean something completely different by "*" than everyone else. Thank you for clarifying that.  You do not have -4 columns, nor -4 rows, so multiplying -4 by -4 in this case is just drivel.  You seem to be confusing numbers and charge.  As I said, electrons do not have negative existence.  There are not -4 of them sitting in a row. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * 4 * -1 positron: the amount of charge in a row/column of electrons. Multiply the row by the column to get the value of the grid: -16. (4 * -1)*(4 * -1) = -16. Where is the refutation of that?

 * Because we either consider 4 rows of total charge -4, or 4 columns of total charge -4, thus 4*-4 = 16. For some reason you seem to want to believe that there are -4 rows of charge.  If you can't see the problem there, I'm not sure I can help you. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * The problem is that you are arbitrarily limiting it to one method. It works for positive: 4 * 1 positron row/column, so (4*1)*(4*1)=16 positron total charge. Value of the column: (4*-1). Value of the row: (4*-1). Multiply to total: (4*-1)*(4*-1)=-16.

 * I am arbitarily limiting it to the method defined by what we mean when we say "multiplication" or "times". If you wish to extend to methods outside that definition, then I think our discussion is kind of moot.  If you don't know what multiplication means, I don't see how you can argue that it is poorly or improperly defined.  This is, again, for about the tenth time, an abuse of both notation and language.  If you want to reduce this to a language game, go for your life, but I have no interest in playing. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * It's argued on -1 * -1 = +1 is Stupid and Evil that the standard definition to which you refer is self-contradictory and unnecessarily convoluted. When we use the correct, principle-opposites-compliant multiplication, the Academian mathematics is proved wrong.

 * Electrons have a negative value where positrons are considered positive. Similarly, if we assigned + to electrons, the positrons would be negative.

 * Of course in your system -1 = {-1,1} = 1 so electrons and positrons have the same charge (which is, of course actually zero, as is every number in your system). If electrons and positrons have the same charge, how exactly are they opposites?  Aren't the really just the same then?  And given that they both have zero charge, aren't they then uncharged, and not actually any energy at all?  So given that energy doesn't exist, does matter?  The answer, of course, under your system, is no. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * Same magnitude, but opposites. They cancel to zero. -1 = {-1,1} = 1 means that the electron (-1) is part of an electron-positron pair, of which the positron is the +1. If they are unified as a photon, that photon is counterbalanced by one travelling in the opposite direction. It all cancels to zero, although the religious zealots controlling the academic institutions would have you think otherwise.

 * Cancel is not the same as equal. The charge on an electron is, by cubic math equal to zero.  That is, there is no charge.  Once again, if you wish to redefine words to mean whatever it required to justify your beliefs, go ahead.  Don't expect me to join you in such a pointless language game however. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * When you quantify how much charge there is on an electron, "quantified" gets -1 positrons and "unquantified" gets an opposite of 1 positron. You are erroneously equating a 1-corner perspective to the 4-corner Cubic truth.

 * You start with 1 on the table -- you experience -1 putting it there, table experiences +1. Take away 2 from the table -- you get +2, table gets -2. ±1 ±2. 1*(-1) - 2*(-1) = (-1)*(±1 ±2).

 * Your persistence with "electrons" as physical concept seems rather odd. It represents a negative amount of electrical charge, not a negative physical existence.  Moreover, charge sign is arbitrarily defined.  We could just as easily call positrons "negative" and electrons "postive" swap the signs, and all would be well.  Doing this with other concepts of physical quantity will not work so well.65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * That's right, the charge sign-designation is interchangeable -- a principle of equal opposites. We notice above, however, with the grid of electrons, the Academic maths gave the wrong sign, due to its principle-opposites-incompliance.

 * Only if you conveniently redefine "*" to mean something else as you have done. If you do the calculation in the normal manner no such inconsistency arises. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * 4 electrons (number of them) * -1 positron (charge per electron) = -4 value for a row/column of 4 electrons. Multiply a row of 4 by a column of 4 to create a grid: the result should be -16. Academian mathematics is incorrect in that it gives +16. The "normal manner" appears to require the calculation to be performed in such a way that it doesn't expose the flaw. Please explain any non-arbitrary limitation invalidating the method I have used.

 * Multiply the charge per row, by the number of rows. How many rows are there?  Are there -4 rows?  If there are -4 rows are they antimatter rows?  Or are they rows of positrons?  What do you mean by -4 rows of electrons? 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * 4 rows = (4*+1) = 4 rows of positrons. -4 rows = the electrons. Value of the row is -4, value of column -4, -4*-4=-16.

 * If you don't know what it means to calculate areas by multiplication I can't help you. If you don't know what multiply means, as you apparently do not, I can't help you.  Have fun in your language game.  I suggest you start by defining black to be white. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * I do know what you mean by "calculate areas by multiplication"; you are referring to the 1-corner Academic multiplication, invalidated in -1 * -1 = +1 is Stupid and Evil. You need to respond to the actual argument rather than employing strawman arguments.

 * I need to see the physical concepts where it doesn't work in order to evaluate them.

 * Generally 3 apples is not the same thing as -3 apples. If we swap the sign and say that 3 apples on the table are really -3 apples then things fail to operate in any manner that accords to reality.  This is not complicated. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * 3 apples. You take them from the plastic bag and put them on the table. The table's increase of 3 is counterbalanced by the bag's decrease of 3. Table gets +3, the bag -3.

 * Or what if they are on the table the whole time, but you count them to determine that there are 3 of them? Then they are passing from "not counted" to "counted". "Counted" gets +3, and "not counted" gets -3. Again, a ± overall result.

 * Does that mean there are then -3 apples in the bag? Or that there are now -3 apples that are uncounted?  If I put 3 apples on the table do I now have -3 apples?  Under normal mathematics this would work as follows: I have 3 apples.  I put them on the table, this transitions me from the state of 3 apples, to the state of 0 apples.  You could say that this is a "transition" of -3 apples, but transitions are not objects, and I do not "have" -3 apples, I have exactly zero apples.  The "transition" is instantaneous (and purely theoretical) and doesn't exist in any physical sense.  Yet we are discussing a system that is meant to represent physical quantities.  If you claim your system is about transitions that's all very nice, but that in no way refutes anything to do with the mathematics of quantity (which is to say normal mathematics) nor provides any useful information (as can e seen by the fact that all "transitions" are instantaeous and result zero - which is to say your system where all transitions are zero.  It tells me nothing about apples on the table. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * For you to have 3 apples, wherever they came from has -3. Or if you count them, "counted" gets 3 and "uncounted" gets -3. Transitions are inherent to quantities, for inherent to quantity-measurement is the transition from "unmeasured" to "measured". You are viewing it solely from "measured", which is a 1-corner perspective.

 * So "-" now covers transitions, and negative quantities and positive antimatter quantities. That's rather more complicated than the standard mathematica version, where it simple refers to negative quantities.  I guess that means you are redefining "-".  As I said, have fun in your language game, I don't intend to play. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * It always covered transitions; when you determine a quantity, "counted" gets +x and "uncounted" -x. From the single-corner perspective, it's only +x. A positive antimatter quantity IS equivalent to a negative quantity of matter. It is indeed simpler than the Academian maths.

 * Continuing, we could consider the 16 positrons to be the opposites of the 16 electrons. If we unify them as energy, we bring the two equations together as 4*4 = -4*-4 = ±16. We thus create the ± result in terms of reality.

 * This is not at all illuminating. It is based on a faulty concept of the charge of a 4 by 4 grid of electrons being somehow "the same" as the charge on a 4 by 4 grid of positrons.  Why don't you try explaining, instead, precisely why 2 apples plus 1 more apple gives the same result as 2 apples less one of those apples.  Once we have simple obvious physical reality down, you can start in with the more abstract physics (which, unfortnately for you, will be invalidated by your "arithmetic system" anyway).65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * 2 apples: you take them from your plastic bag and put them on the table. You get -2, table +2. Take away one apple from that: table gets -1, you get +1. Add one apple: you get -1, table gets +1. ±2 ±1

 * If I have -2 apples, then presumably if you give me 2 apples I will then have 0 apples. That is not what seems to happen in reality. If you want to have a system which doesn't conform to reality, you may as well create a more interesting one. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * -2 apples means 2 antimatter apples. If I give you 2 matter apples, they will annihilate and cause a big explosion. If you survive, you will notice that a result of zero apples has occurred. -2 +2 = 0

 * So the act of me putting apples on the table results in the appearance of 2 antimatter apples that I now possess? If I take the apples back from the table will there be an explosion?  Why have I never seen this occur.  What do antimatter apples look like anyway?  Apparently every time I move an object I create new antimatter objects while still only having one matter object.  Doesn't that mean there is more antimatter now than matter (as antimatter is getting created, while matter is getting moved.  Doesn't that violate the principle of opposites? 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * When you put apples on the table, the table gets +2 and you -2. If, from zero, you separate a matter apple and an antimatter apple, it is ±1. Antimatter apples look like matter apples, except made out of antimatter.

 * Taking the apples back from the table either results in a new ± pair, in which case no annihilation-explosion; or if you're also including the initial you-to-table transaction, it's ±2±2, which creates a 4-corner rotation of -4,0,4,0. It makes sense, since it's a cycle of the apples going from you to the table and back to you.

 * But I had -2 apples, and I gained 2 apples, so I should now have 0 apples. Similarly the table had 2 apples, and got -2, so it should now have zero.  Apparently that is not the case (though it is the case if the -2 is antimatter apples instead of transition apples).  You seem to have chosen to redefine "+".  Good luck with the game. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * For you to have -2 apples, you put two tables on the table, resulting in +2 for the table and -2 for you. ±2. Then you take two apples from the table, which gives another ±2. There are two transactions here: it's you who has redefined a single "+" as referring to two transactions when in fact it only covers one.

(2) You are working with an ill-defined system. The symbol "*" is not properly defined, and you've stated that you can't (or won't) fully define it. The symbol "=" is poorly defined - it doesn't agree with common usage, nor strict mathematical usage (see inconsistency below). How anything can be meainingful when fundamental concepts upon which your claims are based are not properly defined is quite unclear to me.

 * We are basing it on a clear meta-definition: the principle of opposites. From this, we may determine the actual practical definitions of the operations.

 * Excellent. The correct definition is not obvious to me however.  I can't seem to automatically derive it.  Could you clearly list for me all the "allowed" algebraic operations, and the means by which they are evaluated.  I've asked twice now.  Presumably you can simply state them all as they are easily derived from the principle of opposites.65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * The allowed ones comply with the principle of opposites in that they have no bias towards negative or positive. If this definition excludes an operation, you could rectify the operation such that it is included. You can list them yourself, as it shouldn't be too hard to figure out whether they have a sign-bias.

 * Very hard indeed for me. You'll note our argument, taking 2 different forks, as to whether or not "*" has any bias at all.  Apparently I'm just stupid, but I find it hard to determine.  You still haven't told me how to evaluate "*" anyway.  What is {-1,3}*{2,5,7,11}?  Best that you just list the operations, or point me to a source that does.  If you want rules and derivations for "academian arithmetic" try Principia Mathematica or any introductory textbook to modern analysis.

 * Unlike a set like {-2,0,2}, {-1,3} and {2,5,7,11} don't directly collapse to a single number. That means you must use a set multiplication. You can probably figure out yourself if and how it can be done in compliance with the principle of opposites.

 * Well I tried various definitions and all of them go on to show that all numbers are equal to zero, which is squarely back where we started. No numbers exist, only zero.  You cannot count anything because all quantities are zero.  This does not in any way reflect reality.

 * They do exist, however, because by showing that they are equal to zero, you also show that zero is equal to them. This means that from zero, we may use the principle of opposites to create a whole lot of numbers. It's the dichotomy of existence and nonexistence. Your 1-corner perspective blinds you to the fact that it is truth. Unknowingly, through your explorations you have confirmed the veracity of the following Cubic scriptures:

 * "Why something rather than nothing?" Between the opposites, all things are created. As an entity, they exist only as a big zero, seen from space as something and nothing from every possible view. Apply analytical math to Earth sphere and discover 2 opposite hemispheres rotating in opposite directions - equal to a ZERO value existence. Earth is not an entity, for adding the opposite values cancel each other to no existence. All the universe exist as opposite values. Academic and religious taught stupid SINGULARITY is greatest of all evil, as even humans are created via opposites.

 * Yay for langauge. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * Yay for the 1-corner-word-transcending Cubic Truth, part of which you have been so kind as to verify.

 * One more time, could you just list the operations, and how they are to be evaluated for me please? 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * Acceptable operations are ones that comply with the principle of opposites. You can figure out which ones they are yourself. If an operation is principle-opposites-incompliant, you can possibly create a rectified version that does comply.

 * But this is the point. I'm stupid.  I can't figure them out.  What are they?  Can you list them for me please? 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * I am quite sure that you can figure it out, as it is merely required that they not have a sign-bias. By performing the multiplication x*x, we observe a sign-bias -- there is only +y for both -x and +x. We rectify this as described on -1 * -1 = +1 is Stupid and Evil.

 * Is it so hard for you to believe that I cannot understand the time cube? Is it impossible for you to just list the operations and the means to properly evaluate them in all cases? You've been dodging this very simple request for going on 4 weeks now. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * Maybe you can't understand the entire Time Cube principle, but surely you can understand the extremely simple principle I describe above. Surely it is far from impossible for you to fulfill your own very simple request, so I suggest that you take the initiative to do so.

(3) Your system, as described, is inconsistent. Most obviously from examples discussed, we have the statement 0 = {-2,0,+2}. If we assume that you do, in fact, mean the same thing by "=" as common usage, and standard mathematical usage, we should be able to use the symbols 0 and {-2,0,+2} completely interchangeably. This is demonstrably not so (at least by the rules you have given): 0*{-2,2} = 0 but {-2,0,2}*{-2,2} = {-4,4}. Alternatively 0+{-1,1} = {-1,1} but {-2,0,2}+{-1,1} = {-3,-1,1,3}. From such statements as these (if we presume, counter to appearances, equality between results) it is a simple enough exercise to go on and show that all numbers are equal, and hence all of arithmetic is pointless.

 * "All numbers"? You are going to write equations for every single number, and show that they are all equal? It is impossible, because there is no upper limit (or at least, none yet reachable). All the universe cancels to zero; but due to chaos, the tiny little fluctuations such as 0 = {-2,0,+2} can fractalise outwards and evolve into large, complex systems, such as the one in which we participate.

 * Here's the quick version - I can make a more rigourous version if you like, but refute this first: we know that 2 = 1 + 1 = {-1,+1} + {-1,+1} = {-2,0,+2} = 0. Now for any number you care to name (call it x) I can find a number y such that x = 2y (we just let y = x/2).  But then x = 2*y = 0*y = 0.  Thus every number (no matter what you choose) can be equated (through simple algebraic manipulation) to 0.  Every number is 0.  That makes arithmetic a lot easier.  The result is always equal to zero.  It may not look like it at first, but it will be.

 * Yes it's true, all the universe cancels to zero. However... if you have a whole lot of really really big numbers, your pen will run out of ink or your computer will crash. The actual arithmetic procedures won't be so easy then. All the positive and negative charge in the universe cancels to zero, but it is not such a simple matter to go out there and algebraically manipulate it all into annihilation.

 * There's no need, as even the small numbers are 0. Any number is zero.  I have 42 elephants on my table right now.  Well, I have 0 elephants on my table right now, but that's the same as 42 elephants as 0 = 42 (42 = 2*21 = 0*21 = 0).  Any statement of any kind about quantity in your system is utterly meaningless as all quantities are equal.  If you don't see the obvious implications here, I really can't help you. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * The 42 elephants will reduce to zero when you find 42 elephants worth of antimatter to cancel them out. However, the separation in the universe is of a magnitude that is not easily cancelled back to zero. Thus, we can securely operate from a single-corner perspective; but we must not self-aggrandise and flaunt Cubic natural law, otherwise the Time Cube will extinguish us in a horrific armageddon.

 * The fact that somewhere there are 42 antimatter elephants doesn't change the apparent existence of 42 elephants on my table. Nor does it change the fact that there are exactly 0 websites on the internet that propose or support time cube theory.  Currently there is one cup on my table.  Presumbaly there is also an antimatter cup somwhere.  The catch is there there are also 1 = 0 cups on my table.  Despite the fact that there are zero cups from my table I can still drink from the apparently non-existent cup that is there.  How odd.  Your arithmetic is useless for describing reality in any way, and tells us nothing. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * It tells us that everything cancels to zero, but that zero likewise anti-cancels to everything. Since you are viewing this from your single-corner perspective, you have erroneously concluded that it only involves everything cancelling out. That's not true, because zero also anti-cancels to everything.

 * Cancel, anti-cancel, wibble, floozle, pokwer. If you don't want to use the language ("equal to" in this case) the same way as everyone else, you shouldn't be surprised when no one listens, nor understands the explanations you give.  It is hard to base your mathematics on the previous rigourously defined mathematics when you wish to cease using terms to mean the same thing.  If you don't want to use mathematics be up front rather than using the langauge of mathematics, but meaning something else altogether. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * See -1 * -1 = +1 is Stupid and Evil; sign-biased mathematical principles are rectified on that page. "Cancel" is when opposites annihilate each other, e.g. -1 and +1 cancelling to zero. "Anti-cancel" is the reverse of the cancelling process; the splitting of the zero into opposites.

 * Now, as for the rest: I would ask you to explain precisely what you mean by "fractalise outward". The meaning of the term is not at all clear (in fact it seems more like an effort at obfuscation rather than clarification).  I am quite clear on what fractals are.  I am not at all clear on how you wish to see them applied to this situation.65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * Fractal = to divide; you take the simple one {-2,0,2} and split up the numbers into a set with a lot of numbers happening {-8,-6,-4,-2,0,2,4,6,8}. Once you get very many of them it will be rather a difficult task for George W. Bush to cancel them all out with his Texas Instruments graphical calculator.

 * You are using the word in an entirely different manner than (1) common use (2) technical use. Which renders the word meaningless really.  I can claim anything I like to be true as well, presuming I redfine all the words like "multiply", "fractal", "opposite", "equal" etc. as you have done. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * You can claim anything you like to be true, since if you claim Truth it will lead towards humanity achieving Cubic harmony, and if you claim falsehoods it will lead towards the extinction of humanity, leaving only Cubic harmony. It's our choice which way to go; either way, Cubic harmony is attained. You need to be more specific about what is wrong with the use of "fractal".

 * Well, you could look up Fractal. Mathematically speaking they are objects of fractional (non-integer) dimension.  Generally speaking they are objects that display self similarity and scale independence.  I don't see any way shape or form that you use can align with the definition.  Can we add "Supporters on Time Cube freely and often misuse technical terms" to the time cube page?

 * {-8,-4,-2,0,2,4,8}: notice the similarity and scale independence between that and {-4096,-2048,-1024,-512,-256,-128,-64,-32,-16,-8,-4,-2,0,2,4,8,16,32,64,128,256,512,1024,2048,4096}. Clearly "fractal" is an applicable term. No you can't add that comment to the page, because apart from being untrue, the page is about Time Cube itself and not the characteristics of its supporters. Thus, the comment would be an inappropriate "ad hominem" attack.

 * Those are neither self similar, nor scale independent, except in the most trivial of ways. It certainly doesn't describe how the universe "fractalises outward" from zero.  I suggest this is just further abuse of language as has become standard. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * They are self-similar and scale independent. Please explain why these properties are trivial and why this should exclude them from consideration of fractalic properties. The language is not being abused, rather it is being used correctly, but from a 4-corner Cubic perspective, resulting in enlightenment and salvation of humanity.

 * The point of single-corner arithmetic is self-aggrandisation. You are correct that this is a non-point, since the 1-corner self has a limited lifetime, which renders invalid the notion of self-immortality. From a Cubic perspective, we would want to see past the Self to the 4-corner circular whole.

 * My point is merely this: using your four-corner arithmetic all results are equal to zero. There is no mathematics.  Special and General relativity (which I note you appeal to on your site) are invalid in such a situation.  All of modern physics is invalid in such a situation.  All of ancient physics is invalid in such a situation (no matter how many apples I have in front of me, there are really only zero there).  Rather than being enlightening your arithmetic offers far less understanding of the world.  I can't even count real physical objects anymore.  How many fingers am I holding up?  The answer is zero.  How many corners on a cube?  The answer is zero.  Is 4 significant?  Well, 4 is equal to 0, so it is no more significant than 0, or 1 (which is equal to zero) or pi which is equal to zero) or 42 (which is equal to zero).  From the cubic perspective, apparently, anything is really nothing.  This is obfuscation, not insight. 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * But is insight -- once you take the small step to say anything = nothing means nothing = anything. From 0, you create 4 points that rotate; clockwise as seen from one pole, and anticlockwise from the other (the 2 poles are static-opposites that are likewise taken out of the zero). Once you have the 4-corner-quadrant division, that's all there is; further divisions must occur within one of the existing quadrants. See 4 is the Supreme Number of the Universe.

 * But 4 = 0, and 73 = 0 therefore 4 = 73, so in fact 73 divisions is the same as 4 divisions, and there is a supremacy of 73. Any arguments about the supremacy of 4 require 4 to be in some qay unique or different.  However, in your system all numbers are equal.  4 is no different from any other number.  Thus it cannot be in any way special, unique or supreme.  You have, again, contradicted yourself. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * We are considering the 4-corner-quadrant rotation. The 4 right-angle quadrants correspond to the 4-right-angle corners of the square. The same is not true for 73. Take into account that we are referring not merely to 4 as a number, but to the 4-corner-quadrant division.

 * But there exists no "4" in your system. 4 = 0 = 73.  There are 4 anti-right angles somewhere that cancel and make 0 right angles somehow (or something - who knows how this works in your system), and likewise 73 right angles have  73 anti-right angles, which equally cancel down, and the result is the same.  I'm spouting pure drivel here, but that's the result when you use a mathematical system that has no concept of quantity.

 * That's right; from the south hemisphere there is clockwise 4-corner-quadrant rotation, and from the north, anticlockwise rotation. They are opposites. As I said, it's not just 4 as a number, but the harmonic geometric 4-corner-quadrant division. See diagrams on 4 is the Supreme Number of the Universe; I would like to see your 73-corner-quadrant diagram displaying the same harmonic properties.

 * Ah, but I can because pi = 0 = any number I like, hence I can construct a circle with a radius of whatever I want, anda diameter of whatever I want, and within that circle 73 will give the appropriate angles. Besides, the number 4 can change depending on the gemetry you use. Have you not done any non-euclidean gemoetry?  You do realise that the universe is non-euclidean right?  At least you're not misusing langauge this time, just, apparently, unaware of the broader possibilities. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * Are you referring to spacetime curvature? Earth has radial dilation, and also some rotational warp-dragging. That could curve the 4-corner-quadrant division a little bit. But looking from the north pole, the curvature is in the opposite direction to how it appears from the south-pole perspective. Those two opposites cancel to zero curve and a perfect 4-corner-quadrant Cubic harmony.

(4) You freely contradict yourself where nececssary. You state that 5-3=2 is a true statement, but simply a "single corner" view. By the same logic the statment -1*-1=1 is a true "single corner" view. If -1*-1 = 1 is stupid and evil (because it is only a partial result, and not the full result), then I contend that 5-3=2 is stupid and evil. In fact, it is merely an exercise in tedium to go through and demonstrate that any (and all) arithmetical statements are stupid and evil.

 * It is indeed stupid and evil to view the single-corner perspective as absolute truth. As Dr Ray said: "'Takes village to raise child'. Educators are evil people; words corrupt principles, 'takes child out of family' & 'takes village out of child' - 'empowerment of self-evil'. There is no God in 2 x 4x4 femininity and masculinity 2 sex Cube hemispheres, as life is a 2-Cube crap-game."

 * There is no contradiction; the single-corner perspective is considered true under evil Cubeless beliefs. Under the Cubic truth, it is recognised as being but a single point of a 4 point, 4 quadrant universal harmony.

 * May I then correct the page to state that Gene Ray considers the statement 1+1=2 stupid and evil? That's only a one corner perspective, so clearly it is wrong and evil.65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * Yes, you are correct. To my knowledge, Gene Ray didn't say it himself, so it would be best for you to describe the mathematics we have been discussing and how it implicates 1+1=2 as 1-corner.

 * I'd rather use the phrase "stupid and evil" really. I'll fix the page now. 65.95.160.205

I've tried to contend other glaring issues of less global significance where they arise below. 65.95.173.54 22:44, 3 Mar 2005 (UTC)

Old discussion follows:

I am puzzled by the mathematical claims. He claims that $$-1\times-1=1$$ is incorrect. Such a question cannot really be resolved without understanding what we mean by 1 and $$-1$$. 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 $$R$$ such that

 * $$1\times a = a\times 1 = a$$, for all $$a\in R$$

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

 * $$(-1) + 1 = 1 + (-1) = 0$$

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

 * $$0 = (-1)\times 0 = (-1)\times(1 + (-1)) = (-1)\times 1 + (-1)\times(-1) = (-1) + (-1)\times(-1)$$

thus $$(-1)\times(-1)$$ 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}.

 * My basis for {b,c} was if you had, say, {-1,1} + {2} = {1,3}. Perhaps in your sense there is no {2}, but only {-2,2}?  But then is {-2,2} the same as {-2,0,2}? And what of {-3,-1,1,3}*{-2,2}?  Is that the same as {-3*2,3*2} or {-1*2,1*2} or {-3*2,-1*2,1*2,3*2}?  What of even larger sets like {-8,-6,-4,-2,0,2,4,6,8}, which are constructible under the rules you've provided?  It remains quite unclear how this sytem works.  I don't think I can discuss any mathematical statements involving "*" very well when I don't really know what the symbol means.
 * 65.95.173.54 19:07, 26 Feb 2005 (UTC)

 * Since {-1,1} + {2} = {1,3} involves 2 being added to each element in the first set, we could represent it as { -1+2, 1+2 }. As I said, I am not sure about how one would multiply sets not reducible back to a single-number. I think {-2,2} is essentially the same as {-2,0,2} since the zero represents the average and total, but it would depend on whether the operations could be used to equate them.

 * I am defining "*" the same as how it is generally used, except with the principle-opposites-incompliant bias rectified.

 * See Above. 65.95.173.54 22:44, 3 Mar 2005 (UTC)

 * You still haven't actually defined how to evaluate the operation. It is not clear to me, despite being based on the "principle-of-opposites".  Can you please be clear? 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * Operation of multiplication must have no sign-bias (bias towards negative or positive) in order to comply. |-1 * -1 = +1 is Stupid and Evil shows how outcomes of ±1 are derived.

 * I asked 'For example, what is {-a, 0, a}*{b,c}', but you still have not answered. The linked page does not even come close to answering this question. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * I told you: "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}."

 * Nope, that way lies ruin. Following that definition leads to a completely inconsistent system.  Although as you have that already and don't seem to have issue with it, perhaps it doesn't matter. Define it how you like, the correct answer is 0, as 0 is the answer to every calculation in your arithmetic.  65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * It all cancels out to zero, but zero-anticancels out to it all, and so on and so forth. Your 1-corner oppositeless perspective prevents you from following the reduction through to its opposite, expansion, and through to magnificent Cubic harmony.

 * 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.

 * I am struggling to work a lot of this out based solely on the principle of opposites, which is my problem, unfortunately. It is a little unclear to me how I should be applying the principle.  For example, I could argue that of the four multiplications -1*-1, -1*1, 1*-1, 1*1, exactly half produce a negative result, and half a positive result, and thus there is balance between the opposites without need for your constructions.

 * But if we separate them into pairs -- -1*-1 and +1*+1, and -1*1 and 1*-1, with each pair containing opposite statements with regard to signage -- there is an imbalance. -1*1 and 1*-1, being identical (independent of the order), would have to both equal ±1 for correct oppositivity. -1*-1 and +1*+1 could possibly equal -1 and +1 respectively; there is, however, the issue of consistency, as displayed in the graphs on -1 * -1 = +1 is Stupid and Evil.

 * -1*1 and 1*-1 are, however, not identical - why does order of terms not matter? There are many (in fact most) constructions where order is important, a simple example might be quaternions, but there are many many others.  You are aritrarily saying they are the same.  The only reason you can say they are the same is because they happen to equal the same thing: but that is the whole point.  Your decision that there is imbalance is arbitrary. 65.95.173.54 22:44, 3 Mar 2005 (UTC)

 * The quaternions page gave order-dependent outcomes as being negations of each other. Clearly this concurs with the outcome of ±1 rather than a single sign. Anyway, even if the order was important, the grouping is still applicable -- a group of two same-sign-multiplying operations, and another of different-sign-multiplying.

 * It does not concur as sign matters in quaternions, yet does not matter in your system. If you want another example, try the Symmetric group.  There are no signs involved there at all, and yet order of "multiplication" is vitally important.  The end result, anyway, is that we have 2 sets, "same sign multiplication" and "differing sign multiplication" and each set has the same number of elements.  One set produces +1, the other set produces -1.  There is perfect balance between those two sets.  Thus multiplication has balanced opposites, and there is no need to use ± anywhere to create an artificial balance of opposites.  Your assertions are still not justified. 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * No, because same sign is +1*+1 and -1*-1 -- we observe that both signs are equally represented within that group. But the results, both +1, represent only positive -- a bias is evident. The same with the differing-sign; signs equally represented before the operation, but not after, revealing a bias.

 * Symmetric group involves matrices. These, I have not explored in connection to Time Cube. However, what we are discussing here is single-number multiplication, meaning that the matrices are irrelevant.

 * The Symmetric group involves permutations, not matrices, and basic arithmetic can be derived as a special case of an infinite symmetric group, so it does apply. Matrices make for a good example though - they aren't commutative either.  And of course scalar arithmetic (what we're talkign about) is simply a special case of matrix arithmetic (it is the restricted case of 1 by 1 matrices), so again, it is relevant here.  In general order of terms matters.  In our particular case the same result occurs regardless of order of terms, but that's no reason to say that order of terms is in general irrelevant.  There's plenty of reason to count -1*1 and 1*-1 separately, which means multiplication is a balanced operation according to the principle of opposites. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * I will need to see the actual derivation of the order-dependence of single-number multiplication. However, looking at the y=x2 graph, we notice that x is represented in both + and -, but y only in +. The sign-bias is evident. Make it y=(-x)*(+x) or y=(+x)*(-x) and we get only -y for both + and - of x. Again, it's a bias.

 * Derivation of order dependence? Okay, how about -1*1 and 1*-1, purely as symbols, are clearly different.  To assume they are the same is to make an assumption about the meaning of * and how it is evaluated.  You may as well say that -1*-1 and 1*1 are the same (as they evaluate to the same thing). 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * -1*1 and 1*-1 are different if the * is order-dependent for the single-number multiplications. I need to see the derivation of that single-number multiplication order-dependence.

 * And what is your reason for assuming, apriori, that * is not order dependent. In general any binary operation is order dependent.  In particular cases it may prove to not matter because the result, regardless o the order, is the same.  You are saying that -1*1 is the same as 1*-1 (obviously different symbols) because they both equal -1 (the same result regardless of order).  By the same logic -1*-1 and 1*1 are the same because they both equal 1.  There still isn't any imbalance here, unless you choose to force one. Which apparently you do.  Why is it that you need to find imbalance?  I have a perfectly good explanation for why they are, in fact, perfectly balanced... your devotion to imbalance seems almost religious... 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * As I said: "However, looking at the y=x2 graph, we notice that x is represented in both + and -, but y only in +. The sign-bias is evident. Make it y=(-x)*(+x) or y=(+x)*(-x) and we get only -y for both + and - of x. Again, it's a bias." The imbalance clearly exists. "*" ain't order dependent because if you take a rectangle and rotate it 90 degrees, it still has the same area. L * W = A the L and W are interchangeable.

 * Alternatively I could argue that -1 is the opposite of 1 only with regard to the operation "+", and that with regard to the entirely different operation "*" the opposite of 1 is 1 (while the opposite of 2 with respect to "*" is "1/2"). What is the opposite of 0?  Why are you applying "*" to opposites under "+"?  These are different operations.
 * 65.95.173.54 19:07, 26 Feb 2005 (UTC)

 * It relates back to the initial concept of negative and positive; having created that dichotomy of numbers, the two opposite sides should be treated as equal. In nature, negative and positive charges, north and south hemispheres, etc. show an equality. There is no real-life operation to create more of one than the other, so it would be a fictitious lie for such an operation to be performed within manmade mathematics.

 * Positive and negative are opposites solely with regard to "+". With respect to that operation they are perfectly balanced as opposites.  Relating it to positive and negatively charged particles (which is a mere notational issue) is a complete distraction.  If you want to continue with that metaphor however: when I balance positive and negative particles (or north and south hemispheres) I add them together (there is no concept of "multiplication" involved) and thus they are balanced only under addition.  The very concept of a negative particle multiplied by a negative particle makes no sense unless you redefine "multiplied by".  In integer arithmetic to say "n multiplied by m" means to add together m lots of n.  How does such a concept work for negative particles?  Your appeals to physics are merely obfuscation here.  65.95.173.54 22:44, 3 Mar 2005 (UTC)

 * I notice a month later you still haven't dealt with charges of redefining terms for your convenience. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * "In integer arithmetic to say "n multiplied by m" means to add together m lots of n" n*m=m*n add together n lots of m. Interchangeable; the order dependence is an arbitrary stupid and evil single-corner perspective.

 * 0 does not have an opposite, rather it encompasses an opposite pair. So for instance, you can split it into -1 and +1, which are opposites.

 * And under multiplication (an entirely different operation, with an entirely different concept of "opposite") 1 encompases an opposite pair, you can split it into "1/2 and 2". You seem averse to dealing with division at all.  65.95.173.54 22:44, 3 Mar 2005 (UTC)

 * But take into account the principle-opposites-compliant definition: we would get {-2, -1/2, 1/2, 2}. 1 may be viewed as a single element within a 2-element pair grouping: {-1,1}.

 * That doesn't account for the fact that 1 doesn't require an opposite with regard to *, in the same way that 0 doesn't require an opposite with regard to +. 1 is an opposite pair with respect to *. 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * There is imbalance though. How do you separate the -1? It would have to be -1/2 and +2 or something. A bias.

 * But when we redefine the * to be principle-opposites compliant, we notice that the negative and positive are appearing when we use it to create opposites.

 * But - and + are only opposites with respect to +, opposites with respect to * are different. This is pretty fundamental.  It's like arguing that human population is not balanced with regard to north and south hemispheres.  Is the world about to fall apart because the population of the northern hemisphere is greater than that of the southern hemisphere? 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * The mass difference caused by the imbalanced is most likely negligibly small; it could also be counterbalanced by something else. Anyway, what does that have to do with it? The bias is evident: positive multiplication-splits to positive and positive, but negative to negative and positive. Clearly it's an imbalance. Wassup wit dat?

 * People are no balanced. The number of people in the northern hemisphere is different from the number of people in the southern hemisphere - the bias is evident: population splits to be mostly northern hemisphere.  Clearly it's an imbalance.  Wassup wit dat?

 * An insignificantly small imbalance. Either that, or counterbalanced by something else, or a combination of the two.

 * Interestingly if you get the facts you'll find that the population of the northern hemisphere is between 4 and 5 times that of the southern hemisphere -just taking the 25 most populous countires (and considering anything that straddles the equator to be completely southern) the north population is 4.95 times that of the south. I think that is hardly insignifcantly small.  What is it counterbalanced by?  Or perhaps population opposites separate differently than the northern hemisphere/southern hemisphere divide?  If you split the world into appropriate east/west hemispheres the balance works out.  Likewise opposites separate differently for * than the +/- divide.  If you split numbers according the whether their modulus is greater than or less than one the balance works out. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * Hemispheric distributions of population, landmass, etc. are affected largely by Chaos, as well as by the perfect Cubic principles. That's how evolution works; it's the combined effects of Chaos and Time Cube.

 * Okay, this is just to silly not to reply to. The page grounds this in terms of fractals such as the Mandelbrot set, or Julia sets, both of which have complex numbers (that is, imaginary numbers) as a fundamental element of their construction: they don't really work eithout them.  You're supporting your theory using an advanced theory that uses, as its basis, something you have declared to be in complete contradiction to your theory.

 * The fractal is just an example; but it is an example of imaginary numbers representing real concepts, see below.

 * I don't understand your objection to imaginary numbers anyway - aside from the name (which was a weird historical accident) there is nothing imaginary about them. They are used regularly to properly describe real world phenomenon in electrical engineering, signal processing, quantum physics, chaos theory etc.  Many of these seem to be theories that you use to bolster time cube, yet they fall down without imaginary numbers.  I suggest you ignore the "imaginary" part of the name and consider that they are quite observable in the real world, albeit mostly in fairly advanced fields.

 * The numbers are imaginary, because, for instance, under the Academian rules it's impossible to equate i to any real number (i = (-1)1/2 is arbitrarily deemed invalid in order to cover up the contradiction). See -1 * -1 = +1 is Stupid and Evil. They're evident in the real world probably because the calculations being performed move beyond the single-corner perspective to some extent. So it's necessary to expand the 1-corner system to a more complete perspective, but to affirm the dominance of the 1-corner mentality, the extra numbers required are deemed imaginary.

 * Other than that, can you explain what you mean by "negative multiplication splits to negative and positive"? The meaning of these phrases is not at all clear. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * You separate -1 to -1/2 and +2. They multiply to -1 under the Academian laws. -1 multiplication-splits to - and +.

 * It is a separation in the sense that they must multiply back together to give what was separated. Spitting the definition of separation in this context backas a contradiction is pointless.  Go back to your language games by yourself. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * No it's not a contradiction, neither pointless. Consider the reverse of the process of separating an object; it shows that the individual pieces join back together to create the whole. It sounds like you're thinking from a limiting 1-corner self-word-god-perspective.

 * 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.

 * This doesn't really help my understanding, could you actually list, explicitly, and enumerate, the permissible operations (and how they are formally evaluated)? This doesn't really resolve the issue that your usage of "=" is required to be different than the standard one, or else your arithmetical system would appear to be inconsistent.  For example, we earlier applied manipulations that gave 0 = {-2,0,2}, so in theory these objects are equal, identical, and interchangeable.  They are not.  The resulting arithmetic system is inconsistent (and hence you can prove anything to be true).  I presume you do not intend to have an inconsistent system, and hence I assume you mean something else by "=".

 * 0 = {-2,0,2} -- it's true, because a photon has zero electric charge, but you can split it into a positive and a negative particle, thus creating a positive and a negative value from zero. And the "equals" is two-way -- you can likewise bring the positive and negative particle together and they will annihilate back to energy. The system needs to represent real-life.

 * I need to see actual examples of inconsistency in order to evaluate it.

 * It is not difficult to find inconsistencies - they abound. See above for a couple examples. 65.95.173.54 22:44, 3 Mar 2005 (UTC)

 * Let's try a few simple manipulations:

 * 5 - 3 = (1 + 1 + 1 + 1 + 1) - (1 + 1 + 1) = 5*1 - 3*1 = {-5,+5} - {-3,+3} = {-5-3, -5+3, 5-3, 5+3} = {-8, -2, 2,8}

 * Now let us consider a nice simple real world example. Imagine I have 5 bottlecaps on the table in front of me.  If I take away 3 of those bottlecaps the result is:
 * (a) Subtraction doesn't make sense.
 * (b) I have {-8,-2,2,8} bottlecaps in front of me.
 * (c) The same as if I put 3 new bottlecaps alongside the first 5
 * (d) Other (please specify)
 * 65.95.173.54 19:07, 26 Feb 2005 (UTC)

 * There is a problem here, being that "5 - 3" represents a transaction of adding 5 as well as subtracting 3. If we are focusing solely on the transaction of subtracting 3, then we are not taking into account oppositivity of 5. Consequently, it's only "-3", which represents "±3" in totality -- the table experiencing -3 and you experiencing +3. In calculating the result for the table alone, we use the single-corner 5-3=2, since we are focusing on but one side of the opposites.

 * This is not dealing with the fundamental issues, but rather just obfuscation of them. See above. 65.95.173.54 22:44, 3 Mar 2005 (UTC)

 * No, because the fundamental issue is representing the totality of the situation. If we are representing the transfer of 5, then we can circularly follow 5 and then 3 through the transfer process, yielding 8; if that is clockwise, a result of -8 from anticlockwise perspective; from single-direction perspectives, 5-3 = 2 from you to the table, and -5+3=-2 the other way. I can draw a diagram of this if it is unclear.

 * The fundamental issue is that adding 3 bottlecaps is the same as taking away 3 bottlecaps (according you your arithmetic). I have never seen such thing.  How does clockwise and anticlockwise relate to the bottlecaps sitting in front of me?  I have tried this experiment myself just now.  When I add bottlecaps to the table the result looks very different from when I remove bottlecaps from the table.  Where should I be looking on the table for these mysterious negative bottlecaps? 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * Look in the empty space where they used to be. It's the comparison between their presence and subsequent absence from which we infer the negative. Table gets -3, you get +3 in your hand. Note that your hand has an opposable thumb plus 4 fingers. This is evidence of the supremacy of 4.

 * Now there's a random shift in topic. If the table has 5 bottlecaps and I take 3 of them for myself, how is it that the table then has 8?  We can only really resolve this by saying that all numbers are equal - which we've shown separately anyway.  Everything is zero right? 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * Ultimately it can all be cancelled out to zero. However, if you've split off quite a lot of positive and negative numbers, you can run around in the positive numbers and engage in 1-corner god-word-masturbations.

 * Not just the totality cancels to zero, any subset necessarily also cancels to zero (all numbers are zero). If I count just the matter apples and exclude the antimatter apples I still get zero apples - yet there are no antimatter apples to cancel there - we specifically excluded them from the count.  I would suggest that you're the one engaging in semantic masturbation. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * No, because focusing solely on a subset of positive represents a single-corner perspective. That's where the Academian 1-corner maths fits in. It cancels to zero when you consider the totality of the true Cubic unity.

 * What you are saying, however, is that cubic maths is incapable of focusing on the positive aspect. It is impossible to consider the real physical world, because we must also consider it's opposite - something that, for many objects, measurements, quantities, etc. we have never seen, nor experienced, and have no empirical reason to believe exists.  And once agin "equal to" and "cancels" are not the same. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * Empirical reasons: manifestations of Cubic principles. To some extent, we must think from a 1-point point of view, but we should not claim it as absolute truth since it is transcended by 4-corner Cubicism. And in fact, we should base all our 1-corner thought on the precept that Time Cube is truth, in order to avoid Cubeless nazi self-aggrandising. There is ample logical reason within the Cubic rules. "cancels" counterbalanced by "anti-cancels" to create "equal".

 * We recognise that the result of 2 represents a linear perspective, and only 1 of the 2 opposites on that line. As I said, it's a 1-corner perspective. If we are not dealing with the 5 coming to be present, we represent this by ignoring it in the equations and only showing the ±3 transaction.

 * That doesn't show me where the 8 comes from. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * Table has 5 bottlecaps: +5 for the table, -5 for wherever they came from. You take 3: +3 for you, -3 for the table. Place-table-you transaction is +5 +3 = 8.

 * So between me and the table there are now actually 8 bottlecaps? I'm pretty sure there are only 5.  I've never managed to create more bottlecaps by picking them up.  How does any of this accord with observable reality?  It doesn't.  It is just a sequence of ever more strained word games to try and justify a statement that very clearly has little or no grounding in anything observable. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * Only 5 = you count them, resulting in +5 for "counted" and -5 for "uncounted". That is observable. When you say there are only 5, you refer to the counting of them, rather than the transaction 5 to the table and you taking 3. Clearly there is a difference.

 * Is -3 a transaction or antimatter, or negative energy? You're back to playing word games.  Basically what you are saying is that normal mathematics is the only reasonable way to actually deal with, quantify, and calculate the observable real world.  If cubic math can't cope with the real world, or is only useful for the non-observable non-physical non-real world, I fail to see why I should consider it at all - especially when time cube theory claims to be completely rational, based on Occam's razor (and hence empirically grounded) and completely logical.  By Occam's razor if one corner math is what I need, and all I need (as it seems to do the job perfectly adequately for me) to descrie everythign we can observe in the world, then perhaps we don't need to complicate it by trying to account for mysterious unobservables in a complex system that in the end equates everything to zero, and hence tells us nothing. 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * Normal mathematics suffices from a single-corner perspective, but it is also observable that Time Cube is the Truth; see Talk:Gene Ray for observability/testability. Time Cube is proven; see articles in Time Cube Theory category. If God were proven, we couldn't use Occam's Razor to reject him. Rejecting 4-corner ineffable Truth on the basis of your own 1-corner perception is, quite frankly, an act of utter Word-murder and raping of the innocent minds of children. You would do well to overcome the evils of Academia and recognise the Cubic Truth of the Universe.

 * But the four-corner perspective simply tells me that there are zero bottlecaps in front of me, and when I add 3 bottlecaps to the table I still have zero bottlecaps. I cna remove 25 bottlecaps from the zero on the table (do they appear from nowhere?) and I still have zero bottlecaps on the table.  I don't see how the four-corner perspective tells me anything about reality - it seems to tell me rather a lot less, and suggest I can do things that I can't seem to do in reality (like turning 0 bottlecaps into 2 bottlecaps). 65.95.160.205 00:36, 14 Mar 2005 (UTC)

 * No the 25 bottlecaps aren't going to appear, because from zero a pair is produced, composed of negative and positive. Your 25 bottlecaps were counterbalanced by 25 antimatter bottlecaps, which were seized by Al Qaeda operatives for use in a future terror attack.

 * But 25 = 0, so if there are no bottlecaps on my table (as there are now) there are also 0 = 25 bottlecaps on my table. So where are my 25 bottlecaps? If we need antimatter bottlecaps to have negative bottlecaps, then does that mean that i get 2 antimatter apples (-2 apples) when I put 2 apples on the table?  According to your statements elsewhere that is the case.  The contradictions in your statements are increasingly apparent. 65.95.160.205 02:07, 23 Mar 2005 (UTC)

 * You get 25 bottlecaps by splitting off 25 antimatter bottlecaps as well. -2 apples can be a gain of 2 antimatter apples, also a loss of 2 matter apples. You put 2 apples on the table: table gets +2, you get -2.

 * So when I put 2 apples on the table I create 2 antimatter apples that I myself then posses? Isn't that going to be a problem if I pick the apples up from the table?  You were suggesting there would be an explosion should that occur...  You are making an ever increasing number of contradictory statements here. 65.95.160.205 22:21, 24 Mar 2005 (UTC)

 * No, the 2 apples are made out of matter and exist as part of a matter-antimatter oppositivity. Oppositivity in the transaction is evident in that when you put 2 apples on the table, you get -2 and the table gets +2.

 * So tansition opposivity is different from matter-antimatter opposivity? Doesn't that means * opposivity can be different from + opposivity?  Or are such things only possible when required to explain your version of reality, and not in refutation of it? 65.95.160.205 07:19, 30 Mar 2005 (UTC)

 * No the transitional oppositivity is the same as matter-antimatter, because transition of matter left to right = transition of antimatter right to left. I have shown above how * oppositivity includes the sign-dichotomy when "*" is rectified in accordance with the Principle of 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.

 * Okay, so 2*1 + 1 = {-2,2} + 1 = {-1,3}? or is it {2*1} + 1 = {-2,2} + {-1,1} = {-3,-1,1,3}. We also have 3*1 = {-3,3}.  So that means, presumably, that {-3,-1,1,3} = {-3,3}.  Therefore when we removed bottlecaps in the example before we got {-8,-2,2,8} = {-8,8} = 8 bottlecaps.  I haven't personally witnessed such an event myself, but apparently it is what happens all the time.
 * 65.95.173.54 19:07, 26 Feb 2005 (UTC)

 * See above; there is the issue of whether you are focusing on only one of the two opposites. If you are considering the totality of the situation, you would have to use principle-opposites-compliant mathematics to determine the full set of values.

 * In some cases, we have seen, the Academian mathematics gives a result which is part of the full principle-opposites-compliant results set. So the 1-corner maths is as a subset of the Cubic maths. If this is always the case, then I would expect -1 * -1 to equal ±1, since it would have to include the +1 result from Academian maths. It was the conclusion in -1 * -1 = +1 is Stupid and Evil that -1 * -1 equals ±1.

 * See Above

 * 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)

First off, there is no such thing as an Academian. The word you're looking for is Academician. Let's not redefine English and Mathematics all in one go. That said, I wish to weigh in on several points about your redefinition of squares of negative numbers.

Firstly, the square of a negative number being a positive number is nothing more than a consequence of the axiomatic construction of the real number system in mathematics. As background, an axiomatic system is constructed by providing several, hopefully obvious and self-evident, axioms upon which the entire construction rests. This is the case with the real number system and which I'm about to show. Note further that while we can develop the real number system axiomatically, of which the square of a negative number is a consequence, we may build the real number system from prior principles using Peano's Postulates and prove the real number system axioms directly. However, proving the real number construction from Peano's Postulates is time consuming and complicated and I recommend you read Edmund Landau's "Foundations of Analysis" for a rigourous development of the real and complex number systems.

We shall start off with the most obvious of axioms. Suppose we define an operation, called addition and represented by the + sign. We wish this operation to yield another number, produced from the two operands, which is the same type of number as the two operands. These numbers are collectively called the Natural Numbers and are defined as such because they intuitively represent the concept of number in the world. Thus

1 + 1 = 2 1 + 2 = 3

and so on. Now it is obvious that if I add 1 to 2 or add 2 to 1 that I will arrive at the same number. We wish to give this property a name and decide to call this property the Commutativity of Addition and define it thus

a + b = b + a where a, b are Natural Numbers.

The next obvious property we can might wish to define is the uniqueness of three natural numbers added in succession. Thus (1 + 3) + 5 = 1 + (3 + 5) = 1 + 3 + 5. This property is called the Associativity of Addition and is defined thus<BR><BR>

(a + b) + c = a + (b + c) where a, b, and c are Natural Numbers.<BR><BR>

The next reasonable property we wish to define for addition is that of an element which added to a number yields the number itself. This is a reasonable desire because we may wish to express addition of nothing to a number (i.e. add zero apples to four and you get four apples). We define this property as the existence of an identity element under addition and express it like so<BR><BR>

a + 0 = 0 + a = a<BR><BR>

However, introducing this new number, 0, leads to an important step in the construction of the real numbers. We wish to define a new set of numbers which, when added to the natural number a, produce the additive identity element. We therefore introduce a new operation, that of subtraction, defined as follows<BR><BR>

a + (-a) = 0<BR><BR>

We call this property the existence of an additive inverse. It is an obvious property motivated by the need to express that we have 10 cows, 10 of which have been stolen (ten have been taken away, thus -10) and are therefore left with none.<BR><BR>

Proceeding a little more rapidly now, we wish to express these three properties for the operation of multiplication. We define the operation of multiplication to be a repetitive addition of some number such that a * b implies a plus itself b number of times. It should be clear that the three properties defined for addition should hold for multiplication as well. We therefore define them as follows:<BR><BR>

a * b = b * a (Commutative Property of Multiplication)<BR> (a * b) * c = a * (b * c) = a * b * c (Associative Property of Multiplication)<BR><BR>

Let's pause here to clear up some misunderstandings of what the multiplicative identity element is. Like we did for addition, we wish to define some number (a unique number) which when applied to another number using the operation of multiplication yields itself. We define this number to be the number 1. This is sensible and reasonable because if we take a quantity and wish to express that the quantity is added once then we have the quantity itself. We therefore define the unity element to be this special number and express the following principle:<BR><BR>

a * 1 = 1 * a = a<BR><BR>

and we call this property the existence of a multiplicative identity element. Now, once again, we wish to define a new type of number that, when multiplied by a, will produce 1. We define this number as the reciprocal of the number a and thereby introduce the operation of division:<BR><BR>

a * 1/a = 1<BR><BR>

or <BR><BR>

a * a^(-1) = 1<BR><BR>

By now you're probably seeing just how tiresome this development is; and sadly we need to introduce yet another property before we can show why -1 * -1 = 1.<BR><BR>

The final property we wish to add to our construction is that multiplication is distributive over addition. The property is defined as follows:<BR><BR>

a(b + c) = ab + ac<BR><BR>

This provides the crucial link between multiplication and addition and is the property we crucially need to prove our claim. We proceed by writing a proof using the axioms defined above.<BR><BR>

So, let's write a proof:<BR><BR>

0 * b = 0                       (addition of some quantity zero times is zero)<BR> [a + (-a)] * b = 0           (existence of additive inverse)<BR> ab + (-a)b = 0               (distributivity of multiplication over addition)<BR> ab - ab = 0                   (existence of additive inverse)<BR><BR>

Right, so now what about negative numbers:<BR><BR>

0 * (-b) = 0                   (addition of some quantity zero times is zero)<BR> [a + (-a)] * (-b) = 0       (existence of additive inverse)<BR> a(-b) + (-a)(-b) = 0       (distributivity of multiplication over addition)<BR> -ab + ?? = 0                  (existence of additive inverse)<BR><BR>

And there you have it. If we want the properties of the real numbers to work as we have defined them above (which you seem to accept although I stand to be corrected), then the multiplication of a negative number by another negative number must, as a consequence of the properties, produce a positive number. It is neither a bias to the positive nor a systematic conspiracy by mathematicians to expunge negative numbers from their rightful place. It is a consequence of our definition of our number system that two negative numbers multiplied by each other must be positive.<BR><BR>

It is important to note that this was a hastily constructed axiomatic definition of the real number system. I could have provided much sounder and more careful construction. A fully rigourous development will encompass a small book and it is important to understand the grounding as so much of physics, astronomy and other sciences rest on this bedrock.<BR><BR>

A final point to add is that the above construction is the fundamental basis of virtually all higher mathematics. It is sound, proven, thought through and consistent. While other, alternative, constructions can be valid your site does not represent such a construction. If you feel that you have a good construction of the real number system which conflicts with the one above; by all means show us. We will feel free to show you the holes.<BR><BR>

Note: A friend of mine pointed this site out to me after I arrogantly suggested that mathematics is pretty devoid of pseudoscience. I feel humbled and ignorant. Thanks Johann ;-).<BR><BR>

what a waste of time and resources
jokes aren't supposed to be in an encyclopedia. Please don't feed trolls... oh wait, .... damn!

Eris
It might be worth pointing out that Discordianism maintains that things come in multiples of 5, not 4. Can we perform a unification of 5, 4, and 7-based religions by suggesting 140?

metatrons cube
better idea. actually go for a serious workout on assorted sacred geometry themes. Then you would know that be it 4, 5, 0r 7, the obvious root formulae of all sacred numbers is the simple and standard >1<. And, if we are going to start doing articles on numbers, i nominate 36, 37, 111, 144, and 777. (lol) By the way, please spread the word. I don't know how a bunch of geeks missed this, but time Cube is just a modern reworking of "Metatrons Cube." An Esoteric Judaic schema. Prometheuspan 04:42, 8 February 2006 (UTC)

Retrieved from "http://en.wikipedia.org/wiki/Talk:Time_Cube/Archive" Prometheuspan 04:44, 8 February 2006 (UTC)

Metatron

title: Talk:Time Cube/Archive 1