[^^Fleeding home page] [HYPER-SPACE (mfa)] [SUB-space (ma main page)]Cross Product (explanation)
See also: [L/D] [S/D] See also: [af/art3/pkda2001 - pizoig gaming projects] See also: [Style Sheet for CrossProducts] NOTE: There is no possible return from this page; well, other than the BACK key. Since it is assumed that you arrrived on his page by the process of non-linear thinking; or at least by the process of non-linear querying. On this page: {How to Use/Formulate Iconspheric CrossProducts} {Background to the Cross Product} (genology, concept, etc) {Theoretical Underpinnings of Iconospheric CrossProducts} NOTE: Recent theoretical work on the possibilities of Quadrupple (4-tupple) Cross Products has been suspended due to a lack of funding. Data processin continues - un-abated. AxB :: C (var) --> <concept> See also: -[]- -[Triple Cross Products]- How to Use
How to Use the Iconospheric Cross Prodtuct
Much of this section owes much of its existence to Shostakovich Symphony #11 (as well as to: Liz Story: "Wedding Rain" J.S. Bach: "Jesu, Joy of Man's Desiring" Barry Gibb: "Night Fever" (and nine "tips" of the towel to "colour", "god", and "the beegees") (yep: It was THAT kind of day) -- Thanks, "Gentle Beings", Frank. ) -- Lisp and Ada live!
Quickly: XX x YY (z) ---> thing Interpret "XX" in "YY" terms on var "z" (of domain XX) and it will yield thing For example, if we write: FUT x ABS (time) ---> time travel That is take the futurist POV (point of view) and look at it in absurdist terms and and then operate on the variable "time" (taken from the domain of Futurism) and we get "time travel". That is, it IS absurd to think about time travel, isn't it? But, then there are MANY things that such "iconospheric cross product equations" can produce. That is, futurists have been looking at "time" forever (or as close as makes no differences), but have they ever looked at it from and absurdist point of view? That is a FUTURIST (temporarily?) puts on the hat of an absurdist and then through a pair of absurdist-tinted glasses, re-examines the quite familiar thing called "time. The result is clearly given by the WORD PROBLEM: If a train leaves New York traveling at 50 mph, headed towards Chicago. And at the same time a [different] traing leaves Chicago traveling at 60 mph, headed towards New York. And it is 300 miles between New York and Chicago (as the bird files - obviously un-landen by a saxaphone, but with a catchy tune in her/his/heths head). THEN: How long is a piece of string? or: If a tree (named either Woody Allen, Woody Harrelson, or Rachel Carson) falls in a forest, and no one is around to hear it, THEN What colour IS time? or: If oil will run out in 100 years, then what do we need to do now to insure that we (the we then in the future, thate wee hope wille note curse Us.) to make it pleasant for ducks penguins, monkeys, and other non-door props? Why do i ask this? exactly: I ask it why. (period or semi-colon as per your preference) But; alas, i digress. And now, our feature presenation...Background of the Cross Product
(Geneology, COncept, etc) The basic concept of the cross product space conveyeur is based upon the idea of a VECTORIAL cross product. Briefly: A vector is a line that has both MAGNITUDE (size, length, mass, etc) AND DIRECTION (North, Leftward, <h,k,l>, etc) The direction can be in one dimension, two, three, four, etc. Technically speaking the taxonomy of the vector's family is as follows: 0 dimensions -- point 1 -- 2 points --> a line segment 2 -- line segment + direction --> a vector 3 -- vector + behaviour components in at least 2 dimensions --> a tensor 4 etc The current (standard) definition does not include the possiblities of fractal dimensions as making up the various lines, vectors, tensor thingies; sadly, a short-coming, me-thinks. Regardless, for the purposes of the icon-o-sphere, the cross product is the "thought/idea/precept" resulting from taking one view "times" another. For example, we could cross: Jazx with Art (the first being the so-called PRIMARY variable, the second being called the so-called SECONDARY variable) and we might get: 3 of the many attributes of Jazz ============================================= Jazz -- pattern inter-rupted pattern variation colour color juxtapostion of shades/ wheel colour stripes tones interrupted by lines brightness/ crossing at odd angles darkness line stripes stripes down the highway varying line value down the interrpted by dots (the value with odd highway hiccoughing stripe painter shapes at either of Sesame Street fame) regular or ir-regular intervals There are (natch) no hard and fast rules as to what is placed into the grids. One of the primary goals of the icon-o-sphere is as an idea-organiser / idea-generator / idea-exploder / ... /...///.... These entries could then each be expanded upon to form new streams of creativity. And of course, there is no limiting the process: One could imagine a ordered cross product of THREE variables, having Primary, Secondary, Tertiary variables. One could imagine a non-ordered cross product -- ie, where the two (several) variable are equal in strength and neither dominatates. This is usually lumped under the all-inclusive monicker of "balance" or "equal access" or "fair and balanced" which are in all iconospheric reality bogus to being with. But, it's a start.Theoretical UnderPinnings of Iconsospheric CrossProducts
Metaphysically speaking, i would say that much of the iconopherometry ows much of its underpinnings to 'pataphysics, and of course thus, consequentially to the theatre of the absurd. Analogically speaking, an anisotropic chronospheric crossproduct is like a zeroth order iconospheric crossproduct; but, of course NOT of a self referertial form. [Note 1] (that whole mess handled in the note)The so-called Borges Equations
In every system, the possiblity of so-called "cascade failure" (refered here in more politically correct (and more accurately) terms as "cascase phenomenon" -- which include things like "idea explosion", "dimensional runaway", "mis-translation", etc); refer to the section on Cascade Phenomena, below. A constant poroblem is that once something is started it might never end. An example from physics was that at the time of development of the atomic bomb. It was thought that setting off the bomb could trigger all of the Nitrogen 14 (normal isotope of nitrogen) to fission as well, thus turning the entire earth (78% of the atmosphere) into a giant fire ball. As it turns out, "mistakes were made" and it didn't happen. This topic was treated by the ??author?? (Slaughterhouse Five) in his story "Ice Nine". Thus, a majore concern is cascade phenomenon in the + form; ie, where the cascade keeps expanding without end (or at least a case where the convergence to (finite, definite) limit is so slow as makes no odds. A note on notation is inorder. We treat cascade phenomena by menas of their corresponding equivalents (even if only partially equivalent) in terms of infinite (and finite) series. Thus, we will speak of "+" and "-" cascades. Meaning by this a series which does NOT or TOO QUICKLY, respectively, converge. The writer/poet/librarian Jorge Luis BOrges explored these kinds of "infinity" concepts in many stories and essays; refer to the various popular editions, as well as the so-called "standard edition" interlingual text, under the editorship of Eliot Weinberger as "The Collected Fictions", "The Collected Non-fictions", as well as "The Complete Poems". Specifically refer (googel or chedk the pde HERE) to "The Library of Babel", "The BOok of Sand", etc. -[B&N books]- Complete fictions, etc In the book of sand, we are presented with a book with an (apparently) infinite number of pages. Borges gets the book in a trade for a very rare edition. At first fascinated by the book, he later dreads it (partially due to his realising how dangerious such a book would be in the wrong hands) and he thinks to burn it. But, he is affraid that (since it may well have an infinite number of pages), that the book might consume all of the Earth's oxygen. A direct example of a "+" cascade phenomenon. Thus, the Borges Equations (which apparently, he never got around to wriing down in terms of a formal system; similar to the work of the linguist/polyglot Ferdenand de Sausure (see his (postumously written) "A Course in Linguistics" (french-title-goes here). The idea is that these equations revolved around several key ideas: infinity - but both the un-containable infinity such as the cosmos itself (assumed to infinite), but finite infinities such as "The Library of Babel" and "The Book of Sand". Similarlly, the idea of the "I Ching" in taoism. choice - our old friend free will. This is most eloquently examined in "The Garden of Infinitely Forking Paths". -[www.TheModernWord.com]- interesting site etc That is, Borges builds these ideas on a metaphysical level and from each he creates a fiction which is so close to possible as to leave the reader really wondering if it is indeed fiction. One of the most important of these is given in both the non-fiction essay and the fictional story: "The Library of Babel". Which borrows or is complementary of the infinite number of monkeys working out the complete and perfect version of Hamlet. Local refs: -[Jorge Luis Borges]- (the A/H project) -[Library of Babel]- (the A/H: text + nifty gif!)Cascade Phenomena
Closely related is: Irreversibility: -[scientist entry]- (thermodynamics) Minus Form (implosion) "The Clone", "Fantastic Voyage" Plus Form (explosion) "Ice Nine" "StarBurst" "the grammar" See also: grammar: -[in scientist]- (maths) Idea exlosiotn Dimensional Runaway Mis-translation (commonly refered to by phrases such as "lost in translation" or "it looses something in translation", etc.Notes
(this section only) [1] The problem that arrises here is fairly straight forward. By its very nature a chronosphere must accept the existence (and therfore the extance as well as existince) of time. Now while this is "not really" a problem in converting or Inter/Working between the chronospheric and iconospheric approaches; it is most certainly tedious. Since chronospheridynamics postulates a non-zero value for the time variable, and in the universe of discourse with at least the *theoetical* possiblity of rotating, cylinderical black holes, then one must consider at least the possibility of isotropic time. How this might be solved is far beyond the socpie of the current work (and certainly far, far beyond my understanding of such things). As such, we shall take it as read that any possible chronospheric system is at least *partially* a subset of "certain" iconospheric considerations. Note that iherent in chronospheridynamics with the possibility of time travel to the past, then paradoxes must at least be considered as possible; ie, the conseequences of self-referntiallity in time. This (nominally) leads to time paradoxes. Which are dealt with here: -[FutxAbs(time) --> time travel]- NOtice that in terms of iconsopherometry, such anomolies manifest themselves "merely" as abusrditst projections onto other iconospheric axises. Thus, NOT presening a problem in self referentiallity, which in iconsopheridynamics leads idea expansion. Alghought, it should be noted that such an expansion can (given the correct conditions and/or lack of quenching restrictions) lead to cascade phenomenon; eg, idea explosion, dimensional run-away (which would require direct use of the Borges Equations in OPEN form rather in than in closed form, used here -- see above). So, in summary: We take it as read that a zeroth order self-referential cross product in Iconospheric Space (or even in ANY corresponding k-space), is NEVER going to find an exact mapping in ANY chronospheric system. Approximations are of course possible; eg, partial mappings, mappings with restrictions, special cases, etc. {Back to the TEXT, above} Please use the BACK key on your browser to return to where you were. We applogise for the in-con-ven-ience.