Walking the Cointeger

{note; I was going to wait to introduce the concept of the Cointeger until I posted my (still in-progress) post about Cointegrative Mathematics (which I intended to post only after posting my other (still in-progress) post, "Life-logic part-2". But It begins to seem a bit phony to be so linear about what I post when everything about healthy culture (as with sick culture) is so entangled with and implied in everything else in such a non-linear way.  At any rate, something has happened recently with regard to what I first conceived as only a more narrowly "mathematical" symbol, that made it as much a part of the ritual aspect of healthy culture as its Cosmology, and this blog being in part about sharing some of the experimental rituals of Healthy Culture, it seems appropriate share at least this--mostly non-mathematical--, aspect of the symbol here as well. The following will thus allude to as well as offer a taste of blog posts yet to come and in these I will elaborate and extend a great deal of what I pass over here very quickly--- I-P}

I try to take at least one good long walk in the woods everyday, so I was out this past winter walking after a big snow in a part of the land we call "Monacan land" (after the native humans of this place) and I saw that someone had used the two trees standing in a small clearing to mark the two epicenters of a infinity sign in the snow as a way of turning around going back the way they came. When I saw this, I couldn't help but walk in a circle around that lazy figure 8 and so make the sign of the Cointeger (♾).

So what is the cointeger? Well, as I say above, much  more is forthcoming, about the whole topic of Cointegrative Mathematics and the Cointeger than I have the space or time to go into here, but briefly: just as Cointegrative Logic is a kind of Process Logic/"Phenomenologic"*, the mathematics which follows from it is a kind of Phenomenological, Process mathematics, in which the concept of the Mathematical Operation, (ie adding, subtracting etc) is extended and, as it were, subsumed into the larger context of what I suppose Husserl would call the "a Mathematics of and for the "Life World" together with the cognitive "Operations" that (I imagine he would agree) are proper to it. I describe the cognitive Coordinates in the first Life-logic post here: (http://cointegrative.blogspot.com/2014/09/life-logic-part-one-preliminaries.html)

Anyway, in this new inclusive paradigm, these cognitive numerical operations like counting must be Coordinated with and rooted in, the cognitive coordinates as I have described them if they are to be apart of healthy cognition (in which case I suppose you should call them "Co-operations"--rather than operations, if that is not too amusing to take seriously) .

Thus before you have the operations of adding, subtracting etc, you have, in this new, inclusive mathematics the cognitive Operation of Counting (enumeration). Moreover, before the operation of counting comes the operation of Identification (that is you identity entity X by the operations of objectifying it, stereotyping it, dissociating it form both yourself and the rest of its context, and thus reducing it to a discrete, indefinite abstraction). Of course Life-Logic, Being biased in favor of togetherness rather than being biased, like Aristotelian logic,in favor of apartness, has what you might call a Law of Coidentity (as opposed to the law of Non-identity) in which X and Not-X coidentify each other just as the point and the circle coidentify each other in the correspondingly healthy geometrical gestalt. 

Here we have the implication that counting, as it stands (as well as the Mathematics which follows from it), is an uncoordinated dissociated and alienating process, being based as it presently is, on Identity and Identification and thus on what I am calling "Panic Logic", (after the fight/flight dichotomy implied in condition of "Fright" which I claim to be the emotional/cognitive substrate on which this kind of logic is founded), rather than on the phenomenological coidentity and coidentification of Life-Logic. 

Well, just as Life-Logic does not altogether exclude relatively one-sided, either/or, Identity thinking of panic logic, but rather takes the panic out of it by  normatively subordinating its dichotomies to the more inclusive and coordinated Process Logic in represents, so Cointegrative Mathematics subordinates enumeration and the numbers of enumeration to Conumeration and the Co-ordinal rather and merely ordinal numbers of ordinary counting. 

The essence of these Co-ordinal numbers is the Cointeger**  (♾) As you can surmise, the symbol (which unfortunately, on newer computers might look more like the infinity symbol in front of a disk) is more or less intended to comprise/combine the symbol for infinity and that of zero. The Idea here is that there is, after all, no reason that one has to count in a line. Why not also have--and even privilege--the kind of counting that can be Coordinated internally with the other aspects of cognition, in the way relative "itness", is coordinated with relative "Thatness", "Thisness", and "Whatness", as in the Cognitive Coordinates? To do this you would of course have to turn the number line into a number circle/sphere by postulating the Cointeger, which you can regard as the end and beginning of any counting process***.


Well, obviously, lots of things both precede and follow from (and go along with) all of this, which as I said, I will go into further in the a future post, probably on the Cointegrative.blogspot blog.


But getting back, for now, to tracing out the cointeger symbol in the snow. Since I did it that first time, I've started to make a habit of doing it when I got to that clearing in the woods on my daily walk. It became a little Healthy Culture ritual for me after a while. 

Well a few days ago I was "walking the cointeger" in this way and I realized how much the symbol...well "symbolized"... the essence of Life-Logic, the essence of the Logic or Togetherness and its relationship to the Aristotelian Logic of Apartness and Argument which underlies almost all our discourse to this day.

This is what I mean: In a lot of cultural traditions making a clock-wise circle means invoking (inviting something) and a counter clock-wise circle means banishing (or separating from) something. I was thinking this the other day as I started walking the Cointeger, beginning with the infinity part --if you can imagine this; I started at the outside end of the curve which approaches the center crossing point (thus I was starting by walking clockwise) and affirming "I welcome togetherness". Then at the point where the lazy eight figure crosses itself and begins a counter-clock-wise curve, I said; "...And I also welcome Apartness". Continuing along the path to where it crosses itself a second time, (returning to the clock-wise direction) I said "...and I welcome Togetherness And Apartness..." (by this time I had not only returned to where I began but  continued off of the infinity part of the figure (still going clockwise, to the circular or "zero" part of the cointeger symbol(which looks like this ♾ remember), thus tracing out the symbol in a single line "cursive" line. Finally, as I began returning (still walking clockwise now) to the place where I started I said ..."in the spirit of Living Togetherness...Inwardly and Outwardly...", and, (as I recall), closed with some such affirmation as "ashe" or "so be it"

This is the whole sentence. "I welcome Togetherness, and I welcome Apartness and I welcome Togetherness and Apartness in the spirit of Living Togetherness, Inwardly and Outwardly, Ashe" (or "Amen" or whatever you want).

Well that is pretty much the spirit of Life-logic in a Nutshell. As a logic of, Inclusion, Togetherness, and Recovery, it must (to even be consistent with itself) include, (so as to coordinate and heal) its opposite, that is the Aristotalian logic of Apartness, Denial etc. 

Hopefully, if I have described this ritual right, you can try it for yourself (just make sure you start with the infinity figure and on a clock-wise "sun-wise" curve of that figure.

Now its one of the hazards of this blog that I must understand myself to be (no offence) posting this to what is in large part a collective unconsciousness in which the default is the dissociated, reductionist logic of "Identification" so that the average person must necessarily view in isolation (and therefore completely misunderstand)...well everything in any of my blogs really, including all of the above. I mean my whole thesis is that we live in, what is for the most part, a confused, alienated and phony culture in which the mind,heart, body, and intuition are chronically dissociated from each other and sustained in such dissociation by the competitive conditions of the "home invasion" described in previous posts. Under such circumstances its pretty inevitable that those who don't dismiss the intellectual parts of these posts as too abstract or whatever will dismiss the experimental rituals involved as too simplistic or perhaps even too "new agey" (what ever that is supposed to mean). Even worse, most of those who think there is something to all of this will proceed (probably purely by habit) to try to pick out (dissociate) the parts that they think can be altered so as to be (unintentionally) "co-optable" by sick culture itself in some modified form. 

All of which helps to explain why I post things so rarely.

Nevertheless, its not as though any of this is really very complicated although some of it can be rather involved when you try to put into words. What I am trying do with these blogs (in a balanced way, so that I don't permanently lose coordination with other aspects of my own recovery process--and so bring the process to an end) is to the show, directly and indirectly, the various ways the we have all been "initiated" into a Culture of denial and alienation and how this effects not only our cosmologies, identity-politics, rituals and infrastructure inclusively but the very logic by which we assess, understand and communicate to ourselves and others about what is going on. What you have before you in these posts are just virtual and fragmentary glimpses of a relatively non-virtual process of cultural recovery and I make the posts that I do mostly in the hopes of flushing out the few hard core "healthy culture nerds" (this is the description that I think is least likely to provoke the interest of elitists) , who see that the enterprise of inner and outer healing and cultural recovery that I am calling Cointegrative Science could also just be described as the enterprise of Living with Heart, as opposed just "surviving in denial".  Such people will recognize the extent to which these infrequent posts represent a very small but nevertheless real fire of recovery in what is otherwise a blizzard of denial and so will be willing to join me in the focused (and mostly non-virtual) work and play of sustaining this fire by bringing to it the tinder of their own good will, creativity, sense of humor, courage, conscience, and coawareness, along with the focused resolve necessary to foster the cultivation and growth of any such flame in such an extremely adverse environment as exists today****. 

It seems worth the inevitable dismissals, dissociations, and misunderstandings, if I flush out even one such potential colleague. 

Actually, even that is not really necessary; making posts like this every once in a while is just the civil "step" in a "Life-Dance" that is its own reward, whether anything else comes of it or not (as long as I don't end up sitting down and staring at a screen for too long!)



  
*with the difference that, unlike normal Phenomenology, the phenomenology of Healthy Culture postulates the states of Phenomenaesthesia, and Noumenaesthesia ("Life") etc...of which Husserl and Heidegger et al were evidently no more aware than anyone else (see the post "Good Sense and the meaning of Life here:
 http://cointegrative.blogspot.com/2012/04/good-sense-and-meaning-of-life.html

**The association of the Cointeger with what we call the "Integers", (and also with the "Cointegrative" of Cointegrative Science) is of course not accidental. Coordinal Numbers might also be called "Cointegers". I consider these numbers (this conception of number) to be more basic then then even the Natural Numbers since it transforms the infinity (actually the world "infinity" is replaced by the phrase "the Indefinite" in cointegrative math), as much a zero, and involves a more consciously "rhythmic" and coordinated interweaving of the more abstract with the less abstract cognitive functions. It probably represents a pre-"civilized" (and there-for a less alienated) way of coordinating time and space. Perhaps you could also call the the coordinals SelfNatural Numbers in accordance with the  Shared Self-Nature posited by Cointegrative Science (as opposed to the "Nature" postulated by the dominant kind of Science). As such it is useful for outer (that is infrastructural) healing as well is being conducive to the sanity that seems to have evaded, not only the "great" mathematicians, but the rest of us (perhaps to a lesser extent) as well. I will be showing some examples of the uses of Cointegrative Mathematics vis a vis technology and infrastructure in future posts.



***there always have been problems with both zero and infinity in both mathematics and Logic--even the Aristotelian kind. Besides the more familiar paradoxes of infinity, and attending the project of unifying math and Logic which Godel put and end to, there are things like multiplying with zero, in which you can get the conclusion 6 = 2 thusly : 6 * 0= 0, 2 * 0 = 0, which must mean that 6 * 0 =2 * 0. In which case we can cancel out the zeros, leaving 6=2! (I got this example from the book "Mathematics a Graphic Guide"). Yes I know this involves breaking the taboo against dividing by zero, but my point is that such taboos exist only to disguise the limitations of the dissociated, alienated, and not fully rational form of mathematics and logic being employed. As I will show in future post, disobeying such arbitrary prohibitions, even if only in the interest of conscientious consistency and rigor, leads to just the kind of implications that facilitate the needed reform and "sublation" of our present maths into a truly coordinated and cointegrative "Art of Learning" 


****This list of implied desiderata is accurate as far as it goes though it is incomplete and in need of a fair amount of qualification; for example, "Courage" in our culture is too easily confused with "Bravery". Moreover Coawareness--which is actually central to this whole business--has not even been formally introduced (at least not as such). I'll let the above do for now though, and make further clarification the work of another post... 



as always, I'll tidy this up soon....



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