© 2022 Calum Hazell [![[80x15.png]]](https://creativecommons.org/licenses/by-nc/4.0/) Download: [[Hazell 2022b.pdf | pdf]] &nbsp ## 1. Note _Formal Shamanic Conduct: Zonal Installations in Supernatural Space_ (Agger: EyeCorner Press, 2022)¹ stages an indisciplinary practice out of certain anthropologic and set-theoretic resources. Indisciplinary practices stipulate novel parameters for generic executions of conceptual matter because their aim is to recover (through local performances of) the radical democratic and outside-disciplinary status proper to thought as such. _Formal Shamanic Conduct_ is consistent with this objective and advances, in part, a mathematical fiction. No one set-theoretic construct is applied here, but fragments of wellfounded and nonwellfounded convention, language, and patterns of sense-making are integrated in the service of an anthropological mathematics: a practice of mathematics for studying who and what counts as human where and when. Broadly speaking, _Formal Shamanic Conduct_ simplifies set-theory to an operation of _containing_ human and animal elements in sets, whilst the practice of shamanism is reduced to a mechanism of _traversing_ the thresholds of the sets within which those elements are variously contained. The set-theoretic artefact of containment abbreviates membership relation, and the anthropologic-shamanic one of traversal involves compression of shamanic initiation protocols and affordances amongst the Yanomami, principally due to Kopenawa.² With the exception of the clarification offered at endnote 3, my usage of set-theoretic parlance in what follows is as standard if executed towards non-standard ends. In the first place, the essay models propositions that “The human is an animal” and that “The animal is a human” with formal proofs as means of excavating and clarifying local containments it is going to be possible, via their simple concatenation at a humanimal zonality, to traverse. For their part, the propositions are karaoke versions of well-known songs about humans and animals. The essay is not interested in endorsing the propositions, but in their explication in the service of a formal shamanic practice. “The human is an animal” says “The human is a _kind_ of animal,” expressing containment of the human _h_ via containment in a set of all the humans³ _H_ in a set of all the animals _A_ beside all the others _x_, _y_, _z_ and so on, that is: ∀*h*, _h_ ∈ _H_ : _H_ = {_h_}, ∀ _h_, _h_ ∈ _A_, _A_ = {_h_, _x_, _y_, _z_…} : _H_ ⊊ _A_. “The animal is a human” says 1) “_This kind_ of animal is human,” expressing unique containment of _this_ animal _x_ via containment in the set of all such animals _X_ in the set of all the humans _H_, like so: ∀*X* ∀ _H_ (∀ _x_ (_x_ ∈ _X_ ⟺ _x_ ∈ _H_) ⟹ _X_ = _H_, and 2) “_This_ animal is a _kind_ of human,” expressing containment of _this_ animal _x_ via containment in the set of all of them _X_ in the set of all the humans _H_ amongst all the other humans _u_, _v_, _w_ and so on, so that: ∀*x*, _x_ ∈ _X_ : _X_ = {_x_}, ∀_x_, _x_ ∈ _H_, _H_ = {_x_, _u_, _v_, _w_…} : _X_ ⊊ _H_ . Which is to say “The animal is a human” expresses the unique & nonunique humanity for whatever this animal _x_ is going to be due to the nonproper & proper containment of the set of all this animal _x X_ in _H_, where “&” says perpetually and all at once. This dynamic can be abbreviated in such a way that _for_ every _animal_, _it is the_ only _human_ for itself. The proofs are stepwise architectures allowing retrospective extraction of interstitial human and animal situations and circumstances. These are interstitial because between one another and the (preparatory) colloquial and (subsequent) formal sayings of the proposition to hand. “The human is an animal” generates the circumstances _H_ = {_h_}, _A_ = {_h_, _x_, _y_, _z_…}, _H_ ⊊ _A_ /_A_ ⊋ _H_. “The animal is a human” generates the circumstances _X_ = {_x_}, _H_ = {_x_}, _X_ = _H_ about its first tendency and _X_ = {_x_}, _H_ = {_x_, _u_, _v_, _w_…}, _X_ ⊊ _H_ /_H_ ⊋ _X_ about its second. The humanimal zonality is built out of these, like so: **{(**_**H**_ **= {**_**h**_**}), (**_**A**_ **= {**_**h**_**,** _**x**_**,** _**y**_**,** _**z**_**…}), (**_**H**_ **⊊** _**A**_ **/**_**A**_ **⊋** _**H**_**), (**_**X**_ **= {**_**x**_**}), (**_**H**_ **= {**_**x**_**}), (**_**X**_ **=**_**H**_**), (**_**H**_ **= {**_**x**_**,** _**u**_**,** _**v**_**,** _**w**_**…}), (**_**X**_ **⊊** _**H**_ **/**_**H**_ **⊋** _**X**_**)}** Interstitial circumstances are integrated at the humanimal artefact and secured as discrete expressions via their bracketing (**( )**). The thresholds of the zonality are secured where it is braced (**{ }**). Given their discrete integration, local circumstances need not constitute a special narrative or linear explanation: The prospects for erecting zonal installations are predicated upon scalable tractabilities of the artefact and the circumstances it hosts. Zonal installations are prepared by stipulating collections of circumstances from out of the humanimal plane. This requires removing the parentheses securing definitions of interest and drawing a circle or circles around them.⁴ A collection composes a novel expressive compound serving as experimental object and nickname for a zonal installation. The following installation is interested in the collection “_A_ = {_h_, _x_, _y_, _z_…}, _X_ = {_x_}, _H_ = {_x_, _u_, _v_, _w_…}”. It maintains fidelity to the humanimal artefact by adopting this little string as a nickname and to the malleability of humanimal circumstances by what it does to them. The compound unfolds throughout the installation to which it gives its name. The unfolding of a compound makes an experiential pathway along which a zonal operator would be ramified or undergo. Adjustments, prostheses, erasures delivered on the human and animal circumstances at a given installation are intentional or nonintentional impressions made on a pathway: stumpings of thought, ornaments of navigation, technologies of prayer. ## 2. *“A = {h, x, y, z…}, X = {x}, H = {x, u, v, w…}”* ![[Pasted image 20221220120528.png]] ![[Pasted image 20221220120900.png]] I have prepared this installation by making adjustments to each of the definitions out of which the region “_A_ = {_h_, _x_, _y_, _z_…}, _X_ = {_x_}, _H_ = {_x_, _u_, _v_, _w_…}” – that is to say, its nickname – is composed. I have substituted for the elements _x_ in _A_ and _H_ those _c_ and _d_ respectively, and for _h_ in _A_ an element _b_, because according to the event this installation has been designed to stage, there should be no incidents of proper containment amongst _A_, _H_, and _X_.⁵ Similarly, I have renamed _x_ in _X_ “_x₀_” to avoid recursive/tautonymous structuration of _X_ as regards its unique inhabitant. These adjustments are presented at the stations **I** through **III** above. It will also be observed that, as clarified diagrammatically via **II** and **V**, “_X_ = {_x₀_}” is to say “{{_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}}” due to _x₀_ = {_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}. So “_x₀_” names a collection {_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…} intersecting with (**⋂**) _A_ and _H_ about {_b_, _c_, _y_, _z_} and {_d_, _u_, _v_, _w_} respectively. Intersections of _A_ and _H_ with a being = _x₀_ are detailed at the stations **IV** through **VI** and illustrated with recourse to the items ![[Pasted image 20221219130554.png]] and ![[Pasted image 20221219130604.png]] as regards _x₀_ ⋂ _A_ and _x₀_ ⋂ _H_ respectively. With these adjustments to hand, the expressive compound “_A_ = {_h_, _x_, _y_, _z_…}, _X_ = {_x_}, _H_ = {_x_, _u_, _v_, _w_…}” captures an accretion event _in medias res_: It stages an encounter for the zonal practitioner with a being = _x₀_ who appears to be assembling themself at a world = _X_ out of animal {_b_, _c_, _y_, _z_} and human {_d_, _u_, _v_, _w_} elements. In the terms of this installation, then, the members of the sets _A_ and _H_ do not refer to particular kinds of animals and humans, but to particular properties, qualities, tendencies, abilities. Perhaps at this installation, these elements _b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_ are talking in no particular order about facial hardware, wingspan, deriving joy from the good fortune of others, vocalisation, floppy ears, occupation, autotomy, lacking eyes. And they are the ingredients out of which a being = _x₀_ is gradually becoming, resolving, alighting upon themself at a world = _X_ before the zonal practitioner. Let _A_ contain all animal elements and _H_ all human elements where ‘elements’ are properties, qualities, tendencies, abilities. The animal elements called _b_, _c_, _y_, _z_ and the human ones called _d_, _u_, _v_, _w_ are the properties, qualities, tendencies, abilities with which a being = _x₀_ has been determined to assemble themself. “_x₀_ = {_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}” is to say _as things stand_, or _at the juncture at which the encounter is staged_, “_x₀_ ⋂ _A_ = {_b_, _c_, _y_, _z_}” and “_x₀_ ⋂ _H_ = {_d_, _u_, _v_, _w_},” where _as things stand_ is to say “… at _x₀_, _A_, and _H_ respectively.” The ellipses attached as suffixes to the definitions for _A_ and _H_ indicate these sets contain more elements than those _b_, _c_, _y_, _z_ and _d_, _u_, _v_, _w_ respectively, rendering their cardinality indeterminate. These additional elements, whose indeterminacy is both a qualitative and quantitative concern, are abbreviated with recourse to a proliferation of items ![[Pasted image 20221219131038.png]] populating the sets of all animal and all human elements above. The ellipsis attached as a suffix to the definition for a being = _x₀_ indicates _b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_ do not account for every property, quality, tendency, ability with which they are determined to assemble themself in a world = _X_. Instead, they would like to gradually become less disjoint, to intersect more and more with _A_ and _H_⁶ via determination of some animal and human elements in the sets containing all of them respectively. In my diagram, the items ![[Pasted image 20221219130927.png]] and ![[Pasted image 20221219130956.png]] operate as formal placeholders for the prospective determination of some additional human and animal elements about which a being = _x₀_ would also intersect with the sets containing all of them respectively. There is a being = _x₀_, then, who is intersecting and almost disjoint (and prospectively less so) with the sets of all animal elements _A_ and all human ones _H_ about some elements determined by the names _b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_ they are called. The ellipsis attached as a suffix to the definition for a being = _x₀_ indicates the site from which these names and other names have been and are being derived. The names _b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_ are animal and human resolutions for problems a being = _x₀_ poses of themself of the kind: “What do I like to eat?” “What jewellery do I wear?” “How do I dance?” “Am I confident?” “Do I have tusks?” “Can I breathe in the water?” “What is my fragrance?” “Are my teeth very sharp then?” These problems are structured with recourse to the items ![[Pasted image 20221219130554.png]] and ![[Pasted image 20221219130604.png]] in the diagram above, where dotted circles indicate sites (within the parameters of a being = _x₀_) from which they are posed, dotted lines compose pathways along which they are extended, and dashed circles indicate sites (within the parameters of _A_ and _H_) at which they are animally or humanly received and resolved. So the ellipsis attached as a suffix to the definition for a being = _x₀_ indicates the mechanics of determination of animal and human elements in the sets containing all of them from without them. There is a being called “_x₀_” because they are placed just at their origins, so that the sets of all animal and all human elements are known as “_A_“ and ”_H_“ relative to an origin with that name. There is a being = _x₀_ who orchestrates the accretion event captured (with its various adjustments to hand) at the expressive sequence “_A_ = {_h_, _x_, _y_, _z_…}, _X_ = {_x_}, _H_ = {_x_, _u_, _v_, _w_…}” insofar as they stipulate the terms of disjointness enjoyed between **1.** themself and the sets of all animal and all human elements, **2.** the sets of all animal and all human elements, **3.** the sets of all animal and all human elements and a world = _X_ they inhabit alone: >**1.** As per endnote 6, the sayings “| _x₀_ ⋂ _A_ | < ∞” and “| _x₀_ ⋂ _H_ | < ∞” regulate the intersection a being = _x₀_ enjoys and can possibly enjoy with the sets of all animal and all human elements. Which is to say both _as things stand_ (when _x₀_ ⋂ _A_ = {_b_, _c_, _y_, _z_} and _x₀_ ⋂ _H_ = {_d_, _u_, _v_, _w_}) and prospectively (when _x₀_ = {_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}). There are no prospects for the proper containment of _A_ and/or _H_ as subsets in a being = _x₀_ because a being = _x₀_ is _discerning_ as to the animal and human elements they are determined to stipulate and with which they are determined to assemble themself in a world = _X_.⁷ So there are no prospects for the ellipsis attached as a suffix to the definition for a being = _x₀_ and those attached as suffixes to the definitions for the sets of all animal elements and all human ones to ever meet: a being = _x₀_ will always enjoy some finite intersection with/disjointness from _A_ and _H_ whatever animal and human elements it would determine in the sets containing all of them respectively. > >**2.** _A_ ⋂ _H_ = {} is a fact stipulated out of a being = _x₀_ who inhabits a world = _X_ uniquely about the sets of all animal and all human elements where elements are understood as properties, qualities, tendencies, abilities. _A_ ⋂ _H_ = {} is to say that there are no prospects for the determination of a human element in the set of all animal elements nor an animal element in the set of all human ones. So just as there are no prospects for the ellipsis attached as a suffix to the definition for a being = _x₀_ and those attached as suffixes to the definitions for the sets of all animal elements and all human ones to ever meet, nor are there for the ellipses attached as suffixes to the definitions for the sets of all animal elements and all human ones to ever meet: _A_ and _H_ will always enjoy disjointness from one another whatever animal and human elements are determined in them from without them respectively. Moreover, just as there are no prospects for the proper containment of _A_ and/or _H_ as subsets in a being = _x₀_, so is _A_ ⋂ _H_ = {} ultimately to say there are no prospects for the proper containment of a being = _x₀_ in either _A_ or _H_ because a being = _x₀_ contains as elements those collections of elements {_b_, _c_, _y_, _z_} and {_d_, _u_, _v_, _w_} about which _A_ and _H_ are disjoint. > >**3.** The disjointness of a world = _X_ from the sets of all animal elements and all human ones is illustrated via the expressions “_X_ ⋂ _A_ = {}” and “_X_ ⋂ _H_ = {}” describing the vertical items ![[Pasted image 20221219193013.png]] above. There is a world = _X_ inhabited uniquely by a being = _x₀_ who has been determined to contain in themself elements = {_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}. There is not a world = _X_ containing these elements, but containing only {{_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}}, that is, a being = _x₀_.⁸ So a being = _x₀_ does not share its problems with, or allow them to touch, a world = _X_, but assembles of themselves an architecture for them that they would resist the disjointness enjoyed by a world = _X_ and the sites of their animal or human resolution. _A_ is a library or archive of all the animal elements and _H_ of all the human ones over which there is a being = _x₀_ in a state of survey,⁹ or who is curating them. Which is to say the sets of all animal elements and all human ones, where elements are understood as properties, qualities, tendencies, abilities, are curated of a being = _x₀_ who is determined to discern themself from out of them. There are no elements determined by the names they are called but those curated and surveyed, such as {_b_, _c_, _y_, _z_} and {_d_, _u_, _v_, _w_} respectively, of a being = _x₀_. Thus, as to the question “Whence are the elements at _A_ and _H_ in addition to those {_b_, _c_, _y_, _z_} and {_d_, _u_, _v_, _w_}¹⁰ respectively derived?” the zonal practitioner will respond that “They are derived from a being = _x₀_ in _A_ and _H_ insofar as they are disjoint from them. They are derived from the sets of all the animal elements and all the human ones from without them.” _A_ and _H_ are animal and human continua – horizons of all animal elements and all human ones – observing and observed of their constitutive disjointness at an origin = _x₀_ in a world = _X_. There is a being = _x₀_ for whom the sets of all animal elements and all the human ones compose, across their styles and degrees of disjointness, a _templum_ = _X_. _A_ and _H_ are, in the style of Varro, ‘truthful trees… that within them the regions are set where [a being = x₀ is] to gaze.’¹¹ So that there is a being = _x₀_ who is envisioning a world = _X_ as does the _auspex_ their _templum_, who is painting and navigating a world = _X_ with some instruments that are not of it but, quite discerningly out of _A_ and _H_, in of them. ## Notes 1. _Formal Shamanic Conduct_ can be purchased via [https://www.eyecorner.press/books-recent/formal-shamanic-conduct](https://www.eyecorner.press/books-recent/formal-shamanic-conduct). Calum can be contacted via [[email protected]](mailto:[email protected]). 2. See Davi Kopenawa and Bruce Albert, _The Falling Sky: Words of a Yanomami Shaman_, trans. Nicholas Elliott and Alison Dundy, (Cambridge, MA, and London: The Belknap Press of University of Harvard Press, 2013). 3. In violation of a set-theoretic stylistic convention according to which lower and uppercase renderings of the same characters pick out the same object, _Formal Shamanic Conduct_ adopts a convention such that items _c_ are _nontrivially_ beings contained and items _C_ _nontrivially_ containers for all such beings. 4. The number of circles drawn simply reflects the proximity or distance of the definitions of interest to or from one another at the stock rendering of the artefact indicated above. 5. I.e, _X_ and _H_ ⊊ _A_ ∵ _A_ = {_h_, _x_, _y_, _z_…}, and _X_ ⊊ _H_ ∵ _H_ = {_x_, _u_, _v_, _w_…}. 6. I.e., _x₀_ ⋂ _A_ = {_b_, _c_, _y_, _z_} is to say “| _x₀_ ⋂ _A_ | < ∞” and _x₀_ ⋂ _H_ = {_d_, _u_, _v_, _w_} “| _x₀_ ⋂ _H_ | < ∞” where the items || talk about the cardinality of an intersection and those < ∞ about its finitude. Taken together, the notations of the kind “| _x₀_ ⋂ _S_ | < ∞” inform us that there is a being = _x₀_ who is almost disjoint with such and such set _S_ on account of their finite intersection, and those of the kind _x₀_ ⋂ _S_ = {_m₁_, _m₂_, _m₃_, _m₄_} inform us as to the members (_m_n_) of the intersection they enjoy. Thus, intersections of a being = _x₀_ with sets _A_ and _H_ are both and variously = 4 considering {_b_, _c_, _y_, _z_} and {_d_, _u_, _v_, _w_}. 7. Indeed, _to be discerning in a world =_ X _as to their determination of particular animal and human elements_ is a definition for a being = _x₀_. 8. I.e., a world = _X_ is understood as having a cardinality = 1 (since _X_ = {{_b_, _c_, _y_, _z_, _d_, _u_, _v_, _w_…}}), whereas there is a being = _x₀_ who it contains as its unique inhabitant understood as having an indeterminate cardinality < ∞ and > 8. < ∞ since a being = _x₀_ determines themself discerningly, and > 8 since (as to which the zonal practitioner is witness) a being = _x₀_ is discerning themself. 9. E.g. see (Gilles Deleuze and Félix Guattari, _What is Philosophy?_, trans. Hugh Tomlinson and Graham Burchell, (New York: Columbia University Press, 1994), 20-1) the deleuzoguattarian concept of concept in relation to its components: > A concept is a heterogenesis, that is to say, an ordering of its components by zones of neighborhood… The concept is in a state of _survey_ in relation to its components, endlessly traversing them according to an order without distance. It is immediately co-present to all its components or variations, at no distance from them, passing back and forth through them: it is a refrain, an opus with its number. 10. I.e, as per the ellipses attached as suffixes to the definitions for the sets containing all animal elements (where _A_ = {_b_, _c_, _y_, _z_…}) and all human ones (where _H_ = {_d_, _u_, _v_, _w_…}). 11. Reflecting upon cultic augural practices of pre-Imperial Rome, Varro informs us (see Marcus Terentius Varro, _De Lingua Latina_, trans. Roland G. Kent, (Massachusetts: Harvard University Press, 1938), 275-7) that the geographic/geometric complex of the _templum_ was constructed by an auspex through the recital of a sacred formula precipitating the suspension of a nominated parcel of land from the surrounding landscape. In _De Lingua Latina_, this formula, whose precise wording varied in accordance with the specific motivation of the _auspicium_, is recorded as follows: >_Temples and wild lands be mine in this manner, up to where I have named them with my tongue in proper fashion._ > >_Of whatever kind that truthful tree is, which I consider that I have mentioned, temple and wild land be mine to that point on the left._ > >_Of whatever kind that truthful tree is, which I consider that I have mentioned, temple and wild land be mine to that point on the right._ > >_Between these points, temples and wild lands be mine for direction, for viewing, and for interpreting, and just as I have felt assured that I have mentioned them in proper fashion._ ‘In making this temple,’ Varro summarises, ‘it is evident that the trees are set as boundaries, and that within them the regions are set where the eyes are to view, that is we are to gaze…’