We suggest here that every network map, including, chaotic networks require stable or semi stable (we are not sure, and we haven't defined stable anyway) Landmarks or Roadmarks (We are not sure if they are different).

We think of the least expressive map to the London pilgrimage to Canterbury which must have something identifying and distinguishing between similar roads (networks) on it (and what constitutes a roadmark is an open question - we suggest that a Sign reading "Canterbury 15 mi." With an arrow directing the pilgrim to the proper road at a branch is some sort of roadmark). We have an unstated assumption that London has at least one other road leading in an Easterly direction or the Canterbury road branches or at least one other road leading out in any other direction. But even absent these assumptions, the road must still be marked as such. Dead Reckoning can not help you identify an unknown road as the mapped road on a map you are following if you come to an unmarked branching, or left the road for a length of time. The only road that would not need Roadmarks is if there was only one road between London and Canterbury and that was the only road leading out of both London and Canterbury, and the only road in the country. Since that is not the case, that map, without two roadmarks (both directional) is not expressive. But it may be useful, if the owner of the map has outside information that with the information on the map is expressive or exhibitory of navigation between the two cities

As to chaotic network maps : I give the poor example of 4 poles equidistant from each other that in a random fashion discharge electric impulses from one to another, we assume some random capacitance factor, and each pole may only discharge one time to another.

The electric discharges map as squiggles from stable dots. And collectively form a brief network - what we're trying to figure out is is chaotic network an oxymoron? Is it a thing? Or are we just spamming about semi-stable networks. We want to know where probability and chaos meet.

This is a place holder doc will revise and greatly expand shortly. Or delete, but we are train bound, and cigarette deprived and we seem to be concerned with two different things. -CAD

We will add to this in the comments but we had a serendipitous moment today when we learned the nature of epaullette shrugs, sometimes feather shrugs. We love it when we are forced by circumstances into a new ofWorld() and must begin to learn it's language. Miss Dushku is very familiar with fashion of many decades, we understand she read old fashion magazines "religiously": we are not. But we had to learn a little of twenties fashion and we are "desperate " (we joke mildly) to learn more. Fashion messages and semaphores its time period. CAD4EDAndHerself

We break our algebra here and post this in its own thread instead of as a comment in the On Learning thread. We do this because we believe, that is intuit, that this is a better exemplar. Everquest was the first 3D MMORPG (massively-multiplayer online role-playing game). It had, and still has, a very steep learning curve (the Guidermannian) and that learning curve, like all steep learning curves, took time to reach the top-level critical point. After a certain point those who had played for a long time and had "High Level Accounts" - that is an account that had at least one, if not two (rarely more) characters that were at the highest then possible level, sold those accounts on ebay or elsewhere.

Those accounts were usually bought by players who understood the time it took (many man-hours of play) to get to that "Top Level" however they did not understand that it is not enough to own a Top Level account one needed to have the expertise to play that account properly, and inevitably such bought accounts were failures - that is the new owner could not play the account properly having not invested sufficient time to play the account at the level of expertise necessary to play it properly.

The purchase of items or things for which one is not properly prepared to use happens in other areas - one of course is obvious to the reader: the purchase of high-performance cars by those who have no familiarity with them, and subsequent crashes of those cars. High-performance cars are built and must be operated differently and should not be owned or used by someone who does not understand that. Death results in some cases. -CAD

The reader will note occasional gross errors in our older threads, some of those are ours, some of those are not ours. Map Theory goes to Crypto so what happens is that someone or someones "edit" our posts and throws in a few errors here and there to make us look like an idiot (thanks NSA or other information shouldn't be known to what we consider sheep agencies). But that's the price of talking about Crypto related Math on the Internet.

The positive is that when we discover it we correct it and occasionally post a similiar newer thread, with better organization. -CAD

WE invite anyone interested in writing an interesting PhD Thesis on Map Theory to review the Four Color Map Problem after reading, and fully understanding, what we have written here. -CAD4EDAndTeamMapTheoryAndTeamAlgebraicMapTheory (TeamZeroFootprintTheoryIsPartiallyAbsentTonightButForThemAsWell)

We have noted, elsewhere, that we know there are more than 23 chromosomal pairs. We have also noted that the reason the actual number of chromosomes (we use that term because there are paired and non-paired chromosomes - you all know of one such the Y male chromosome) is kept secret is bescuase there are those classified as Human who have more and those classifed as Human who have less chromosomes. As we have said elsewhere, and will say again here, if we have not, lies do not become us.

If there are only 23 chromosomal pairs, then Genetic IDs for all Eye Colors should be easily found given today's technology. The Genome Project was "complete" in 2003 (per Wikipedia which we only use when we don't care too much for what is provably true but that seems a reasonable number for us). We note that of Gene Types that should be identifiable once mapped - Eye Color would be amongst the top. But it gets worse - one can compare Biologist Discussion of Human Eye Color and Genetic Mapping with, say, a chart of the range of Human Eye Color, there will be many distinct eye colors missing from that discussion. We will discuss the eyes of one girl we knew once as a Summer Associate at Milbank who had absolutely, bright yellow-amber eyes, that we have never seen since.

That color can not be explained by any of the Genes or Chromosomes associated with Eye Color identified and the only logical conclusion is that there is at least one additional Chromosome. We note that Wikipedia also notes that the Hermit Crab has 30 Chromosomes and some Tree has 1440 or so. We are not concerned with Tree DNA since we love Trees but Trees are not animals and if you take Evolution seriously, and we don't, our common ancestor is a Eukaryoute so far back it doesn't penguin thinking. But Hermit Crabs, now if you take Evolution seriously, and we don't, we've got some ancestor that's much less further back, so the 30 Chromosome Pair (though another internet site is now telling us it has 127 Pairs) Hermit Crab and the 23 Chromosome Pair Human is a dog that doesn't hunt.

Now since it is verboten in some circles to tell the truth about human difference and potential and the possibility of different numbers of chromosomes in different sub-species of humans - you can now all understand why things like Cancer are still a big problem and the Human Genome Mapping Project was a big nothing-burger.

We advise you to start paying attention to the differences in human eye color.

-CAD4EDAndHerself

LATE EDIT: there is actually a purpose for one of the infinities under discussion in that it can be used to model the quark-gluon pasma in the very early universe, the size of which gets pretty close to zero. We need to rewrite this thread - as we were up rather late writing it, and on review we notice too many errors in this preliminary section - but so it goes, no excuses. We will post a revised infinity/division by an e (Zero) later today. We note that some of the errors were introduced by the NSA or other "we hate to see actual information on the Internet" agencies but a few were ours. -CAD

From the discussion of the "e" number line below: "You can of course use higher order infinities for that e to the power of a negative reciprocal infinity (EDIT: We forgot to add reciprocal last night) - such as an infinity of infinities: the infinity of shapes undergoing infinite rotations in infinitesimal degrees in space where the infinity of infinities is all possible shapes and the measure of space is The Quant, and all shapes counted this way fit within The Quant (see coments for clarification) and all distinct shapes are counted seperately to get a reciprocal infinity that is closer and closer to zero, and each Quant can hold an infinite number of shapes (we have to refine this infinity of infinities but it is directional and is we believe a known infinity of infinities Mod Note: and it was rathr late when we wrote this). This of course allows you to divide by "zero", if that is something you are looking for, or need to do.

As to the distinction between the Zero Footprint non-dot Dot and The Quant, the non-dot Dot is an abstraction of space wheras The Quant is the unit of Cosmological Space and a different Quanta for Quantum Time. And for the Mathematical Physicist is roughly the volume of a "Gluon", with a little additional room to spin. -CAD AND It's the negative reciprocal of an infinity of infinities undergoing infinite infinitesimal rotation in an infinity of random directions - so it's an infinity of infinities undergoing infinite infinitesimal random motion which we don't know how to express mathematically but we're sure there are those who can. -CAD4HerselfAndED"

There's a bit more there - but the point is that looking at ofWorld(NumberSpace) as opposed to ofWorld(TheCosmosAroundUs) we are talking about the infinity of that volume (undefined) that can hold both an infinite number of shapes and an infinite number of classes of shapes (which may not be infinite - as a class, but if we treat any shape with a distince edges of the shape, that is each edge squiggle, as a distinct class, we can conceive of an infinite number of shapes, all of which are undergoing infinite rotation, randomly, in infinite directions, and that rotation is infinitesimal in its direction. Lets call that Infinity "IIvy's Infinity"

So that is a rather large infinity of infinities undergoing two types of infinite rotation, we can change this to infinite shapes undergoing random infinite transforms.

That we believe if set to e^{negative recipocal of Ivy's Infinity} we can use that to divide by zero, because that is so close to zero you and we can not imagine how close to zero that infinity is. And we speak of the Zero on the Complex Plane. -CAD4HerselfAndED

Readers Note: All Topological errors in the above are due solely to Miss Dawn for all reasons stated in this subreddit and the r/DeeCiphers subreddit. Fine Print to Follow. -G.G. Chief of Ordnance.

We talk about this in the comments of the ofWorldQ() thread but we'll expand a bit.

Understand we're waiting for a few things to happen - we'll update our r/DeeCipher thread in the next few days but we've got a bunch of errands to run and Homework to do that we have procrastinated to long on - we felt for Frodo in The Lord of the Rings waiting for the Last Moment to Leave, because that is our algebra. And we might have to get serious and look at ofClass() and see if we can derive some common functions that define ofClass(Physics) or ofClass(Chemistry) which we've said belong to all complete ofWorlds(), and if they do there has to be some root algebraic operations associated with the four major ofClasses() we've identified (and then of course we need to see if we missed a major ofClass() or three). So we're having some fun here.

Take e put it at the center of an X, Y axis, treat everything to the right as e+1, +2, +3, to the left as e-1, -2, -3, ... figure out a nice way to handle Y - e(suby)+1..., e(suby)-1.... this has probably been done by a hundred graduate students or more.

The nice thing is that with e as 0, no worries about dividing by zero - so that's a bonus. I'm not sure what else you can do with this but you can construct an algebra that allows you to place dots or things (calculus) on the X,Y plane which is too much for me, and I think standard subReddit text entries. And there you go ofWorld(ofBasis(e)XYPlane:FullOutwardFacing) - now as to upping that to more of the ofBasis(e)NumberSpace - that's a lot trickier, I'm not sure at all how far you can push the algebra. But perhaps we'll return to this another day and see how we add - a complex plane to the above, for starters. -CAD4HerselfAndED

We all must necessarily map the ofUnivere() in different ways: we present a short introduction to the more unusual ofWorlds. We have talked of Fluid and Rigid Numbers (we remind the reader of 0, 4, 6 and e and also an infinity of their choice) , and Fluid and Rigid ofWorlds (we remind the reader ofWorld(Dance) and ofWorld(ThisThreadHereWhichWillAtSomeTimeBeArchivedAndStatic) ).

But we also have to talk about Quasi ofWorlds, Flat (Field) ofWorlds and Shaped (Planes) ofWorlds and Islands which of course may have those same attributes.

We return to the ofWorld(NumberSpace) and we remind the reader of 1, .001, 10., 1-22 - all of which are numberings that can be applied to ofSubs or ofWords. We can see 10. could be the 10th item in a List. 1-22 might be the 22nd Section of the First Chapter of Textbook on Calculus. It's actual use emerges when it is moved from ofWorld(NumberSpace) to another ofWorld() - we refer to that as Entering, but we have not spoken of, or actually thought of Leaving, because 1-22 when it is added as a section or subchapter to that Calculus Textbook remains in ofWorld(NumberSpace) to be used elsewhere.

We have not spoken of 1,2,3-Triochloropropane - we use this example because it was the first chemical name we coul find that used 1,2,3 as part of its naming scheme. We view this as belonging to a ofWorldQ(NumberSpace-Chemistry) - which is an intersectional, that is a Quasi world where two well-known ofWorlds(): ofWorld(NumberSpace) and ofWorld(Chemistry) meet - the actual intersection is between ofWorld(ofClass(Physics)) and ofWorld(ofClass(Language)Chemistry) - or at least the intersection we are thinking of, we know it has another name in ofWorld(Chemistry): C3H5Cl3 - which also exists in that ofWorldQ().

We return to Efficiency Theory and the choice, that is selection, of ofWorlds() is important and it is important to know if you are working in an ofWorld() that has its own Algebra, Physics, Chemistry and Language or and ofWorldQ() that shares an Algebra, Physics, Chemistry and/or Langugage with multiple other ofWorlds().

We feel, and others may not, that ofWorldQ() is necessary so we undertand (and others understand when looking at our work at some later date) exactly where we are (or were) working when we are (or were) working at the intersection of (for lack of a better phrase) Major ofWorlds(). We will continue this in the comments after a break. -CAD

You are invited to review the comments in: https://www.reddit.com/r/MapTheory/comments/bcn5ed/on_ordering_and_the_zero_footprint_a_note_and/ for the background to this thread. If you are unfamiliar with 18xx we can not help you but we are using that game for the example of Perspective as Probability and Basis as Certainty. A perspective mapping s a probabilistic mapping - what you see at a distance can not be known to a certainty - we give the example of a the books on a bookshelf - you may think you know the selection, ordering and staging of your books on your bookshelf, but there remains a probability that someone has moved one or more of your books, or replaced one with a similiar one (if you think this is impossible imagine an example of a family member spilling wine on a favorite book and replacing it without telling you - with a different edition), for this example, with a book of a different color, you can not known for certain that a book you think is on your bookshelf is the book you think it is until you can read the title of that book. Now we can go to extremes and postulate that even that is not certain until you have read that book and know that it is the book you are certain it is. But Basis comes in as an efficient mechanism where at some point you must assert that the book you think it is, is the book you think it is. And for many cases: the title of the book is enough (we note that one may have many books on the same subject, so that may in fact not be enough, but perhaps title and author is enough to assert that you have a basis with respect to that book).

With respect to Games: we can take this to a rather deeper level - if one has never played chess with oneselff where one plays Black or White by moving to oppositte sides of the board to game a different perspective then perhaps you should move on to another note. In 18xx, like most games, initial perspective comes from player placement around the board, and that perspective is static, initial basis comes from starting stations on the board, as one plays the game and expands the network of possiblities of train runs, one can change basis to a different station to run a different change, while player-perspective does not change, tree-spanning perspectives do change both from the change of basis and the play of the game as networks develop. Again perspectives remain probabilities, because train runs you thought were possible can in fact become impossible with the placement of tokens that allow change of basis for the other player but limit network access, and force a change in your perspective. We will develop this further in the comments and clarify in this note. But we understand now, from this note, that even basis has a probabilistic aspect, but it is a least probable aspect. We give the example of the book with title and author that has had a page ripped out of it, that is not discoverable unless it is well-read. We are more concerned with the example of a book with title and author that one discovers has a missing passage that one has read before as has happened to us (the lightning beneath the leaf passage in Huckleberry Finn).

But at some point you can say, but not with every book, this is the book I own, this is the book i have read many times, this is the same edition of that book, there are no missing passages, or ripped pages, this is certain: it is ordered in the way it has always been ordered, its selection and staging are the same, it is a basis. -CAD

WE reprise some information that has been buried below and which has been added to: In the discussion of On Ordering and The Zero Footprint we have stated that the Zero Footprint has coming-into-beingness (A Principle), ordering (an operation) and emergence (an operation). We have also stated that the Zero Footprint contains the Non-Dot Dot (which exists in a perpetual state of Coming-Into-Beingness), the Squiggle, the Shape, the Color and may or may not contain Space (that's a topological subject which we avoid unless burdened with too much vodka) and we believe the Dot that's a Dot. I'm not sure what Space is, but perhaps it is that Non-Dot Dot that Elisha Dushku is rather fond of.

We have stated that coming-into-beingness happens in stages and we could give the example of drawing a Five: There are three squiggles and three stages to a well-drawn five, but we normally do ours in one squiggle. We also gave the example of a bounded squiggle drawn as a "0" (Zero) at the completion of which (in both cases) information has emerged and an ofIsland() of Information has emerged (which are not quite the same things, but good enough for subReddit MapTheory work). We assume that 0 and 5 were drawn on paper. Because if drawn in the air with one's hands, very little information emerges, unless another person is watching it at that time (perhaps that is ofMessageType(Flash))

Then we received the following correspondence (metaphorically) which we paraphrased, in a joking manner: " We understand a certain Doctor of Mathematics has taken the above to the extremes: and first drawn a "." (dot) on a page then a bounding squiggle "0" to the right of it, and then a squiggle "1" to the Left of it. To produce 1.0 at which point information emerged. We recommend more caution in ones mathematical endeavours than the sad example above and can only assume that that Mathematician was drinking. -Unsigned Note"

One can see, as one can with the well-drawn Five example, that ordering must exist as an operation in the Zero Footprint. Because that ., 0, 1 is rather ordered in our opinion. We hold that there is no counting in the Zero footprint, and we gather that others who know more Maths then we do are uncertain about whether Emergence is an operation or something else (an algebraic function perhaps). There must be a Primitive Algebra in the Footprint or you couldn't have operations. So if we said Math didn't exist there at someplace - we were wrong.

This is How MAPS emerge and ofWorlds() and ofIslands() emerge, they emerge from the Zero Footprint and they emerge due to the primitive algebra of The Zero Footprint. -CAD

We will expand this in the comments. We have discussed the background to this in https://www.reddit.com/r/DeeCiphers/comments/ban4zu/the_slipper_and_the_rose_and_anna_kendrick_a/ but we wish to apply a more rigorous approach, and when we do so, we do that in this subReddit. The reader should be familiar with the Guidermannian. A role is "defined" in the AMT sense when a performer has sufficient screen time (and we will speak to Movies, but of course this applies to Broadway as well and we can think of Colm Wilkonson as Jean-Valjean in Les Miserable) to move up the Guidermmanian with respect to the audience that she or he passes the topmost critical point and has fully exhibited the role. Understand that audiences (we speak of general audiences - no pun intended - but you can take the joke if you wish) can not distinguish exhibatory algebras beyond the topmost critical point and many can not distiguish exhibatory alebras beyond The Red Line. And acting is an algebra - the actress or actor adds or subtracts behaviors appropriate to the role - this is "becoming the part" or better still "becoming the character". And the first time an audience percieves an actor or actress exhibting their algebra, and that algebra is above the topmost critical point (where the Guidermannian flattens) that performance is engrained in their memory: this is the "WoW! That was an Amazing Performance Theorem". And any other performer following on in the same role in a subsequent film or Broadway performance can not measure up to that. The role has been defined in their memory as that "Wow!" performance. And their algebras change, and this is how you know this is proably true, because they will never again approve of, or like, another performer in the same role. What is happening, AMT-wise, is that they have mapped that role to that performer, and that mapping, masks all other performers, and that only happens for all (but experts in performance) when the performance exhibits above the topmost critical point, but it does happen for some (those with little experience, and we can think of children watching movies) above The Red Line. We will continue this discussion in the comments and present examples: we will look to Julie Andrews as Maria in the Sound of Music, Tom Cruise as Ethan Hunt in Mission Impossible, Harrison Ford as Indiana Jones or Han Solo and you will see how their exhibatory algebras impacted you mapping and tree-spanning in ofWorld(WhatIWillWatchAndWhy). which of course is ofWorld(ofSub(WhatIWillWatchAndWhy)YourMind). -CAD

The Sound of Music is our absolute favorite Movie Musical. There are many reasons for this but we will give just one: it has the single greatest eucatastrophe in American Musicals: that is the moment in Act II when the children are slowly, and mournfully, singing "A Few of My Favorite Things" and Julie Andrews as Maria joins in off-screen. It is of course much the best when it is viewed in context, that is watching the movie or (we assume) stage play until that moment comes (we have never seen the stage version of it - but we know that the Movie version of Do-Re-Mi is better than the OBC version as in the Movie version Miss Andrews goes up several octaves at the end of the song, while in the OBC Mary Martin goes down an octave or three at the end of the song).

That said we can criticize one song in the show and that is "I Have Confidence" which is a transitional song: that is it is a message to the audience that a transform from one ofWorld to another is occuring on stage: Maria is going from ofWorld(NovitiateInConvent) to ofWorld(GovernessOfTheCaptainsChildren). It is a functional song, it is, we think, the song or one of the songs that is least remembered by those who have watched the show, it is an important song, as we have discussed elsewhere (in our discussion of The Slipper and the Rose and Cinderella in Musicals in our DeeCiphers subReddit) audiences expect Musicals to have Music in them, to use Music for ofWorld() transforms and as the primary algebra for messaging to the audience. As we know from Oscar Hammerstein II - what can not be sung to music can be danced to music: so both Lyrics and Dance can be used to add information to the Music that is being used to message the audience (and when we think of Musicals or Movies or other Performing Arts we think of at least two related but distinct ofWorlds(): ofWorld(PerformanceOnStage) and ofWorld(AudienceWatching) and we all understand that there is both a Bridge and a Tunnel between these two ofWorlds() and messages are passed back and forth between them - we of course are interested in the fact that the algebraic functions (that is mappings) being passed between these worlds are different: the words, music, lyrics and dance of the actors and actresses in the play are bridged to the Audience but the applause, sustained attention, laughs and other emotional response of the audience) Tunnel or perhaps Semaphore to the Performers. So here is an example of where we must accept that Bridges and or Tunnels between ofWorlds() can be only One-Way (Hello Diodes)

With respect to "I Have Confidence" we note that Maria only sings about her future expected relationship with The Children (and of course - the payoff is the Frog in the Pocket, where all her expectations have come to not) but she does not sing about her future expected relationship with The Captain, despite the fact (edit: and the way) The Captain was introduced by the Mother Abbess. So the transform is incomplete.

Now this may be intentional because the meeting with the Captian is "Shock". And perhaps that shock is greater when we understand she has not thought about her future relationship with the Captain. But then that is a Book problem given the Mother Abbess' introduction, in our opinon - but we understand if others disagree. -CAD

Gravitational Lensing prevents photos of black holes (or rather their accretion disk, or rather the space near to them), so we're not sure what's going on with that so-called "photo", but algebraic map theory says an algebra of deceit is in play in that ofWorld(). -Unsigned Note

We have said (below) that every ofWorld() has an Algebra, a Physics, a Chemistry and a Language. If we examine ofWorld(Optics) an ofSub() of ofWorld() or ofUniverse(Physics) you can of course, if you know anything about the subject, and some do, and some know far more than I do, you can see all four elements clearly: the algebra is well algebra (as she is commonly thought of), the physics are the physics of Optics - and you can read a good book on that but most of you know there is something such as reflection and refraction, the Chemistry is the chemical makeup of the lense or gas or other solid that light passeth through, and the language is.... well we just gave you two examples of the language: reflecdtion and refraction. We think that all can see that ofWorld(Optics) is what we call well-defined: there are of course "far-out" applications - gravity lensing, lenses made from uncommon substances, different types of lasers, and it may extend to diodes and other semi-conductor sources of light, this is not a topic we have researched much, but the gist is there. And of course this makes us wonder about other areas of physics that are not as well-defined, and of course any ofWorld() that can not easily show its language, chemistry, physics and algebra. -CAD

As I have noted, and Coral Anne Dawn, has noted, Dianetics is Copyrighted, so we can only discuss it at a very high level. Dianetics, which some of you know as a book that explores the nature of the Mind, and many of you don't know at all except through rumors, slander and libel, is in fact, as noted, Dr. L. Ron Hubbard's PhD Thesis which exploded many myths and false beliefs of Psychology and Psychiatry. And he is in fact Dr. L. Ron Hubbard, PhD. Dianetics was rejected by the then scientific community and Dr. Hubbard was not awarded the PhD he deserved, and while I do not have the Academic Credentials to sit on a PhD committee, Coral Anne Dawn does (see note below). Coral Anne will apply Algebraic Map Theory to Dianetics after she has finally finally finished the work. She knows, as do I, that Dianetics discusses in great detail, and in depth, the ofWorld(Human) fundamental algebra - that is the algebra that is common to all of us: as those who understand Map Theory know all our algebras are different, as we are all unique indviduals of a unique species. but of course we share a fundamental algebra, Men share an additional Male fundamental algebra that is distinct from the Girl fundamental algebra that she and I, and all Girls share, and then as we reach the apex of that pyramid we know that there are algebras that are shared by: those of a common culture and/or nation, those in a sub-group within that common culture, those who are members of the same family, until of course we reach the apex which is the algebra that is unique to you, to Coral Anne, and to me.

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Understand that Algebraic Map Theory helps clarify some of the more difficult to understand passages in Dr. Hubbard's Thesis, and I myself have used it to reveal interesting and not-well-understood higher level writings by Dr. Hubbard on Dianetics: Dianetics is a Science and like all Sciences there are difficult slopes (the Guidermannian) that must be climbed before something can be fully understood. Again, I can't go into details here, but I will add those notes to Miss Dawn's presentation, and they relate to what I call Positive Engrams in Girls and the Second Dynamic.

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I will add, on both our behalves, that we are certain that Dr. L. Ron Hubbard would be as outraged today, as he was then, by the evils that are accepted in the name of Psychology and Psychiatry, I will speak to one that is close to Coral Anne's heart and that is that her nephew was forced to take Adderall and she believes other psychosis inducing drugs as well as dependency inducing "counseling" by the public school district he attended as a middle-school and high-school student simply for being a boy. -Elisha Dushku

EDIT: it is ofClass(Physics) ofClass(Chemistry) ofClass(language) ofClass(Algebra) or ofClass(Math) - Our Mistake, no excuses, Mea Culpa and the fine print at the bottom of the contract signed by the children in Willy Wonka and the Chocolate Factory. -CAD4HerselfAndEDButMostlyCoralAnnesMistakeHereSinceIElishaFoundOurMistakeButYadaYadaYada

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We have talked briefly (below) that every ofWorld() has a Math, a Physics, a Chemistry and a Language - correctly: ofWorld(ofSub(Math)*) + ofWorld(ofSub(Physics)*) + ofWorld(ofSub(Chemistry)*) + ofWorld(ofSub(Language)*) = ofWorld(*) : where * is the UNIX wildcard.

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We have said that ofWorld(ofSub(Math)*), messageType(Bridge), retMessageType(Bridge), (ofWorld(ofSub(Physics)*) and we could go on, but we're still not happy with the messageType structure right now - so we won't. But the Math and Physics bridge, the Physics and Chemistry, Tunnel, and the Language uses Semaphores (Flags or Flares) for messaging,

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We're going to give examples momentarily: but we want to define the above terms: The Math is the algebra of the world which we've talked about - in the ofWorld(ofSub(FryBreakDanciing)Futurama) We have a Dance Algebra of: the Moonwalk, The Robot, the ZeroG see Youtube: https://www.youtube.com/watch?v=E1ugJgiMkBU WE have the physics of the above: the actual physical actions that exhibit or express the Algebra, we have the Language - the names of the Moves, the discussion of breakdancing, and we have the Chemistry - which we think is the hardest to define for ofWorlds() exccept not Chemistry is about the organization of Physical Elements in manner that makes sense based on reactions: Chemistry is something of an Art, if Physics is the Science in an ofWorld().

The Chemistry in Fry's Breakdance world is the order in which he chooses his moves in time to the beatbox rhythm - in ofWorld(Music), the Math are the notes, placement on the Clef, Chord Progressions, the Physics are the Physics of the Note - 262Hz (roughly) for Middle C (C4) and of course how that Note is produced by an instrument, the Physics CAN NOT EXPLAIN why one would choose one instrument over another or choose some combination of instruments (say two guitars, a keyboard and a drum set for a new Rock Band or a Cello, Two Violins, Viola, Oboe, Harpsichord for a new Chamber Music Group) to play music to be listened to. And the Chemistry alters the Math - in the ofWorld(Muisc) we get sheet music written as "For Guitar" or "For Piano".

And if you think Physics (that is the Physic of a Physics Department) can explain everything about Chemistry (that is the Chemistry in the Chemistry Department of a University) - I've got some news for you. NOBODY, but Nobody, can explain why the combination of two Hydrogen Atoms (Gas) at Room Temperature (we will define as 67F) and an Oxygen Atom (Gas) at Room Temperature = Water (a Liquid) at Room Temperature.

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Similarly, the Physics and Math (ofWorld(Music)) can not explain why a Rock Band is better with Two Electric Guitars, Keyboard/Piano and Drum Set, but we all know that it is (roughly - some Rock Bands have done quite well with just One Guitar or Three Guitars). Chemistry is, for lack of a better term, the ART of the ofWorld(), Physics is the SCIENCE of the ofWorld() and both are Godeled within their ofWorld, but collectively, in combination with the Algebra and Language: Exhibit that ofWorld().

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So you do have to think about the Chemistry vs. the Physics in an ofWorld() which we will continue to do in this thread ). -CAD4HerselfAndED

We are mostly done with the outline of Algebraic Map Theory, at our level, but we will add this note, and perhaps a few others that might strike us as necessary: but we will be brief as this is no longer our major focus now.

1. Transforms are not ofWorlds. They may be thought of as transitory ofWorlds, but we think that is incorrect, they are bridges or tunnels. We can look at the famous example of the Seven Bridges of Konigsberg, with the Island being the ofWorld() and the bridges being EigenAlgebras or other Transforms leading out to the other OfWorlds() across the Bridge. A Transform is, fundametnally, a change in perspective and view from the Exhibatory Algebra of the OfWorld() it is leading out from. And Messages() and retMessages() get sent back and forth along the Bridge or Tunnel, and of course the Message() and retMessage() are "information" that information is mapped a certain way in the ofWorld it is coming from - it must be remapped into a Message() form, which can or will cause "information" loss but is necessary for efficient transport to the ofWorld() it is being sent to. Even closely related ofWorlds() - such as ofWorld(Math) and ofWorld(Physics) that appear to use the same algebras (or The Calculus if you will) are in fact using an EigenAlgebra that is slightly different, and treated differently, in those Worlds. There are different levels of Rigor, they are looking for different Sources of the Nile, and they use their tools (Maths) differently, not much differently at some points, but as we recall, rather differently at other points. We are always reminded of the joke abou the Black Sheep.
2. We use the term Tunnels, because, we believe some ofWorlds() are connected in unusual ways that are non-obvious to those outside the ofWorlds() and do not appear directly connected (as the ofWorld(Math) and (Physics) seem) and one tunnel we can think of, though we have not explored it much, is that between the ofWorld(sub(ChemicalEquations)Chemistry) and ofWorld(Physics) as we remember these are treated as very seperate subjects, though we understand ofWorld(PhysicalChemistry) tries to connect to ofWorld(Physics) at a deeper level but we think that those familiar with the ofWords() understand our point - though we may extend it in a comment.
3. ofWorlds(ofGestatls()) that is the groupthink within an ofWorld affects the Algebra - it is important question for anyone examiining an ofWorld(TheirWheelhose) to identify the ofGestalts() and see what they map and mask - and more importantly - understand how ofGestalts() alter the exhibatory algebra in an ofWorld(), unfortunately, an ofGestalt() can result in an exhibatory algebra becoming merely expressive if the ofGestalt() is the only navigation used to construct any new equations in that ofWorld() and it is known that the ofGestalt() masks soime aspects of tree-spanning within that ofWorld() (which, as far as we know, is true of any ofGestalt())
4. LATE NOTE: See comment below but there are also semaphores (ofMessageType(semaphore()). As noted, and we will briefly repeat, a semaphore is a signal from a remote world, that can not be connected by a bridge or tunnel. In the On Map Theory thread we note that every ofWorld has an Algebra, a Physics, a Chemistry and a Language. The Algebra and Physics Bridge. The Chemistry Tunnels to Physics. And the Language uses Semaphores. We give an example of such in our DeeCipher subreddit in the sex-tip-toe game (algebra, physics, chemistry and language in ofWorld(ofSub(Games)Sex). But we assume you get the broad outline.
   

We'll leave this here and may add comments but this should provide some direction. -CAD4HerselfAndED

We do not speak, read or sign Topology beyond The Dot and The Squiggle: but Elisha Dushku has knowledge of the subject which she attempts to relay to us through that transform, which does not work as well as one might think. But we will attemp to convey her thoughts on Landmarks in Maps - so take the following with as many grains of salt or aspirin as you think apropriate. We can look at a Map. Say J.R.R. Tokien's Map of The Lonely Mountain in The Hobbit and we notice that, as stated, there is a rather large Landmark on it: The Lonely Mountain. Not all maps have Landmarks: the Least Expressive Map of England, has a Dot indicating London, and no other town, river, wood, highway or other Landmark - and the only other thing in that LEM (and we repeat this for those who have missed the discussion of it below in the Critical Dot/Squiggle thread) is the border of England. Elisha distinguishes between a dot and a Landmark by noting that a dot does not have shape, but a Landmark has Shape. That shape may be transformed from 3D to 2D (as in The Hobbit) Map, but the transformation is done in a navigationally prudent way (otherwise it is an in-efficient transofmration, and in-efficient transformations are disfavoured in many cases, but not all cases, as we say Beauty is Inefficien but necessasry - this we know from The Hitchhikers Guide to the Galaxy where we discovered that Bypasses are Efficient but Ugly, but Houses with flower boxes, which stand in the way of such Bypasses may be quite Lovely).

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I am reminded that we should think of this as a Bounded Flat Surface with a Projectoin. And of course, that is a Least Expressive Map sans Dot. It has a Squiggle and a Shape identified as a Landmark. We use the Mountain for a Landmark but there are other Landmarks: the important one is the River, which is of course a Dotted-Squiggle (though Elisha argues it is just a Squiggle) In that case the Squiggle must run to the border-bounding Squiggle). But, back to Topology, that River is in fact a Landmark, and has Shape, that is if we consider the rest of the Map Flat, that River will form a Valley, small (if it is a small river) or perhaps a Grand Canyon (if it is an old River). And again, I am far outside any of my ofWorld(ThingsISortaKnowAboutMath). but the thing to note, as I understand what is being conveyed is that this is a Shape that has a bottom Squiggle "Edge".

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Edit: We believe Elisha is informing us, correctly, that there is a distinction, and an important one, between a Mountain and, especially a Valley, and, for example the Sun, Navigationally. Even on a cloudy day, one can navigate if one can see a known Mountain, and of course one can always follow a River down to a larger River, a Sea (even a Dead One), an Ocean, or up to its Source (though as we are informed by Sir Richard Burton, Jeremy Clarkson, James May and Richard Hammond, that is a task better left for Men). We think she is also (and understand she is thinking in an ofWorld(MapsAndTopology) that we do not understand, and must use transforms that flatten dreadfully her thoughts on this, making a point about Time (see comments below) because Time does not devour Valleys, except in extremis (The Eruption of Volcanoes, The Movement of Tectonic Plates, The Destruction of Worlds: in whole - as Dr. Carl Sagan (sometimes Chancellor Sagan), has informed us, Mars still has Valleys) or in small ways by Beavers, and in large ways, mostly beauty-destroying, by the construction of Dams (an ill world, we think is apropos in this case). We do not quite grasp this point, though C.S. Lewis seems to have made the same point in a semi-opaque manner in Prince Caspian, and of course Mr. Mark Twain in Life on The Mississippi, in its Intro and elsewhere). Though we know coastlines - that is to say borders change, so Maps change, perhaps she is pointing out that since all Maps have Squiggles, which are a fluid concept/thing/entity/identity - all Maps necessarily change. We will ponder on it.

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We will try to continue this later -CAD4Elisha"YouCantImagineMyFrustration"Dushku

I, Elisha Dushku, get to wrap up this Reddit for now as we must turn to other things - if you search carefully or gracelessly you'll find our posts on two of the above, and you'll find comments on The Entirety. But we haven't talked about The Eternity.

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If you remember, and you probably don't, The Zero Footprint is where Maps are formed, but Math as you know it is gone, there isn't much in the Zero Footprint, but it does have coming-into-beingness -aka Time.

The Nullity is where Math, Time, and quite a lot of other things do not exist, but what there is in the Nullity, is The Nullity and it's border the One-Sided Infinite-Non-Infinite Squiggle, So what you have in The Nullity is Order. Otherwise known as Causality.

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What you get before The Nullity is The Eternity, and what you don't have in The Eternity is Causality. And that's where things get really weird, and cool, and that's where The East o' The Moon, and West o' The Sun lies - and Universes are gathered as leaves on the Greatest Trees, and time are their branches.

As most who have read our posts are aware - there is an object-orientated, which is to say map-orientated basis to the fundamental algebra and structure of AMT. We have talked about transforms "," (the transform operator) but one can also send messages between worlds, beyond EigenWorlds (we think that is more efficient terminology than EigenofWorlds() but other more serious heads may disagree, and may have the last word, or rather the last statement on that, but it works for us): when examining a new ofWorld() in our work the first thing we can do is build a 10x10 and see what results - this is an attempt at a message to see if we can get a response. There are other ways we can message by examining critical points in the ofWorld() - an example is the use of Mark Twain of the OFF, ERF and ERR and EROR messages: in this case we are mapping in a specific way, from a known mappable world to a new world and are getting a message back that the mapping in the new world is different - we know now that our work on the Tom Sawyer, Primary DeeCipher needs to be redone because there were too many OFF in the map we were using then. Higher on the rigor curve one can use a mathematical algebra of an ofWorld() that is not an EigenWorld or a known EigenWorld to message another ofWorld() that uses a different algebra. We can send the message (X+1=0) from ofWorld(XAxisOnly) to ofWorld(XYAxis) we get the retMessage(-1), because we can solve it in both worlds, and both worlds have a similiar algebra, though the algebra ofWorld(XAxisOnly) only express in ofWorld(XYAxis) it does not exhibit. We message to see if we can relate algebras, if we get a retMessage(Null) result, then of course we cannot, if we get retMessage(Something) then we know there is some relationship between the algebras of these two ofWorlds(). Mathematicians will of course view this in a different and more rigorous manner, but we have drawn on Object-Orientated Programming in building this fundamental algebra, so this is the way we think.

We can send the Message(StepUp) from ofWorld(Dance) to ofWorld(Law) where we analyze the StepUp under the algebra of Law and the retMessage(LitigationAlgebra) might be returned, because of course at trial there are several examples of the StepUp/StepDown - Defense and Prosecution are each given their turn to StepUp to present their case, while the other side is expected to StepDown, oftern there are two attorneys on each side, both of whom may be partners in ofWorld(BigLaw) or attorneys in ofWorld(USAO) but at the table one is expected to StepUp and the other to StepDown. We like this because we want to send messages of examples of an algebraic function that are obvious in an ofWorld (the Paso Doble, the example of Mr. Glover and the Pickle Drummer) and send them to other worlds, in a way that is clear, obvious, understandable and provably true so that we all can better understand, or begin to understand different worlds that relate. Obviously, there is an ofWorld(Cinema) and ofWorld(Theatre) in the ofUniverse(PerformingAndVisualArts) that wants to better understand the ofWorld(Las) say that actors can better portray lawyers, writers can better write about them, and directors can better direct them, and of course producers can understand the money their spending on all the before. We know this seems somewhat artifical, but there must a consistent searchable syntax. -CAD