Forms of Life and Cultural Endowments
2023; University of Illinois Press; Volume: 18; Issue: 2 Linguagem: Inglês
10.5406/19446489.18.2.02
ISSN1944-6489
Autores Tópico(s)Historical Linguistics and Language Studies
Resumowhat does it mean when we speak of a form of life? When speaking of a form of life, we consider one different from others by way of its mode of expression, that is, by its means of construction. This interpretation lends itself to a functional analysis of the material put to use and whose operations jointly express the concept we are after. Modes of expression can be plotted between a rhetorical and semantic axis (Gates 48). As such, “[t]he level of connotation of the visual sign, of its contextual reference and positioning in different discursive fields of meaning and association, is the point where already coded signs intersect with the deep semantic codes of a culture and take on additional more active ideological dimensions” (Hall 56). Coordinates within this domain encode signifying practices, revitalizing the traditional concept of signification as a function of what's signified with respect to a signifier. The content of a syntagm in this coordinate system, a point in this plane, indexes its function with respect to others. As such, we will conceive of the content of modes of expression functionally.A function is defined by pairing an element from a domain and another from a sub/co-domain whereby that pair is an element of that function. In this way, we can treat functions as abstract objects. If we treat a domain as what determines the availability of an expression, and a sub/co-domain as representative of its range of application, then the function of applying some proposition maps a movement from a domain of selection to one of composition, that is, its use with respect to others. The function of an expression, then, represents an operation over the possible worlds of its appropriate application (Taylor 201–02, 269, 276). This becomes more interesting when considering assertions whereby one subject is known to be the case for another, a concept that's modeled when a proposition from one is appearing in the object position of another (Fara 65–73). Resultingly, a proposal for an ontology constituted by modes of interaction rather than identity stipulations to physical entities arises. It follows that if a form of life is understood by way of its mode of expression, then its content is expressed as an ensemble of the functions of its operations. Let this ensemble of functions be called an endowment.There is a pervasive debate in cultural studies that obsesses over proprietary notions as well as the ability to locate an origin. With that in mind, let us consider a coordinate system where there are two perpendicular axes, and we define positions within the space provided at the intersection of lines drawn from each. Each axis is represented by an ordered series of markers. A line drawn from each axis indicates that the coordinates indexed at their intersection is a function of these two markers. This locates an individual at a point in that domain, indexing a relation between the axes framing that space. Therefore, that coordinate-wise space, here a domain of possible expression, is not “empty” as pessimists would claim, but is filled with functional-content, albeit functions yet applied and marked by a point in that plane.Although we are currently speaking of two-dimensional space, the same follows for as many dimensions as we want. A point's location is a function of three values in three dimensions, four in four dimensions, and so on. Forms of life, then, will be comprised of four dimensions. This allows for a space-time conception, wherein joint expressions bend space-time and that space dictates those individuals’ possible movements. From this, we construct a geometrical model of space-time represented as a cube composed of two-dimensional slices with these slices extending in a particular direction like cards stacked one on top of the other to model time.We want our conception of a form of life to be spatial. After all, it is its “form” we seek. We can conceive of one function as different from another given our perspective within that space. Our being situated within that space is revealed as a function of the space between one point and another. If we were not a member of that space, we would not have the ability to discern between these two points. We would only conceive of the space as a whole, which, nevertheless, would be a point in our space-time leading to an infinite regress or contradictions. More on that later. From here, a triangulation can be made from our position with respect to the other two, for these functions’ difference is understood by way of the distance between them, assuming they're viewed from the “right” angle with respect to our position. Those points being expressed as a function of coordinates (a, b) and (c, d), by the Pythagorean theorem we understand the distance between them as sq-rt((c–a)2 + (d–b)2). If we go to higher dimensions, for example, (a,b,c) and (d,e,f), we add the square of the third difference to our formula—for example, (d–a)2 + (e–b)2 + (f–c)2—and take that sum's root. We can do this for however many dimensions (note: time = distance/constant, so spacetime2 = c2t2 – d2). These three points are now related in a way that covers a triangular space organized around these coordinates in this plane, indexing a domain organized around these coordinates. It appears that given multiple functions, there are operations that we can perform on them that give us the shape of the space they cover. A three-dimensional sphere is the set of all points extending a fixed radial distance from a known center-point. Take the three-dimensional example above and set it equal to the radius; knowing the values for the central-coordinate, solve for the remaining points to complete the sphere ( = circle in three-dimensions). A cube, then, is composed of squares in each dimension whose sides are a measure of the distance between its corners. And so on.With each shape mapping the extent to which a form of life obtains, how then do we consider the affairs within that state? How do these functions interact? Following our definition of a function, we must consider what it means to be a member of a particular domain of functions bounded by these edges ( = distances) in multi-dimensional space. Our consideration must be able to explain how we characterize operations over functions. It must contain a definition of operations to define a constant ( = point by location), a successor operation ( = enumeration), and what composition ( = joint application) entails. If an individual within that space is indicated by the function of its location, we understand that individual by way of an injective relationship, a correspondence from its domain to others. In other words, these correspondences represent its range of interactions ( = affairs). A form of life's domain, then, can be considered closed under recursion ( = infinite use of finite means) and composition ( = interaction).The above amounts to the question: What can one do with(in) a form of life? What follows will also help us model how a form of life assumes different shapes dependent upon its internal affairs with respect to its environment. These “affairs” are able to be modeled poetic computationally (Peterson 3). They are expressed via a function from a domain of selection into one of composition. Thus, given coordinates n, to formalize a point at which that individual is that individual with the least assumptions is to formalize when f(n) = n, making n = 0. As such, f(0) = constant. It follows that successive expressions from that individual, instantiating its being a member of a particular domain, are represented f(n + 1), for n = n, so f(n) = n-successor. Given these conditions, it follows that if n = 0 is a member of some form of life and for all n, if n is a member, then so are n-successors, then all n-expressions are members of that form of life. In other words, if 0 has a certain property, and if 0 has that property, then its successor has that property, thus all members of the class denoted by that property also have that property. The zero, then, is a member of that series, the base upon which all identified expressions as an extension of that subject are constructed, present but not always represented in the output. This represents how we'll conceive of subjectivity by way of subject continuity. For the same subject can obtain, given the forms of life in which it participates, multiple properties indexed to the respective framings of those properties relevant within a form of life. More on that below.A conception of the affairs of individuals emerges now that we have conceived of recursion and subject continuity. Composition comes from considering a function whereby the output of that function becomes the input of another, thereby characterizing a joint operation. From this, we can consider the same form of subjectivity producing different output dependent upon the sub/co-domain ( = context) of identity projection ( = assertion). The union between individuals within this space can be easily modeled for a point with no other by which to consider it just is that point, but a point m such that m + (n + 1) yields (m + n) +1, a context in which both are members. Pairing follows from a point paired with no other produces no other point. However, m * n = (m * n) + m. Pairing ( = multiplication), as well as pairs of pairs, are built up from union ( = addition). We find that if we encode operations (Diagne 62) to be projected into domains, that will then be decoded in a manner relevant to that domain's form of life (Hall 3–4), then via the recursive operations above, projections obtain ( = register) within another form of life—are identified within the domain of another—only when n > 0 and do not when n = 0. The latter does not negate the individual, for 0 is the constant determining that form of life, recall the function of n prior to projection is n. A zero merely denotes that the subject's identity does not obtain within those affairs. So as far as interaction is concerned, we can posit that an individual and its identity within another's form of life jointly obtain only when both are positive via pairing. We conceive of this OR that subject when at least one projection is positive. It follows that a form of life cannot be known ( = captured) in total, although understood by way of its mode of construction unto itself.As such, we are concerned with forms of life in-formation. The formation of collections of affairs whereby we can discern one form of life from another are info-theoretically called ensembles (Shannon 63). Here, we call them collective improvisations, following the work of Amiri Baraka. From the above, we can model different conditions within that domain. A subject produces different output dependent upon that form of life's relation to others. Conditions for appropriate projection follow from considering a normalizing function ( = BOOL: if r(n > 0 then 1, else 0) that if the function of a projection n obtains from some operation r given two forms of life characterized by functions g and h, then: f(n) = g(n)*BOOL(r(n)) + h(n)*BOOL(r(n))By determining f such that g results when r is positive or h when r is 0, this composite function states that IF r is positive THEN g, ELSE h. Either that subject obtains an identity within the composite form of life indexed by f or does not. This more complex function is the result of composition that can be defined in terms of recursion. The IF/THEN, ELSE operation determines the extent to which one can interact with forms of life determined within our geometric consideration of our state of affairs.A form of life can be considered closed under recursion and composition; however, through these operations, we can see a rather unintuitive point that is cleared up when considering the above poetic computationally. The volume of that form of life will always be more than its surface area, that is, superficial appearance. There will always be more operations possible within a form of life than can be characterized from a point external to that form of life. So, when talking about forms of life poetic computationally, the operations composing its shape are understood by the enumeration of the functions by which its output is identified with respect to others.Consider a list such that e represents the combination of operations that express a function f in which case e represents the components of f. We can enumerate a list of these functions within that particular form of life, formalizing our concept of an endowment below. For example: e0, e1, e2 . . .f0, f1, f2 . . .Horizontally, these enumerated lists can be treated additively. Their value separately can produce 1 or 0 with respect to some external form, encoding the space of that endowment pointwise so that all that has to obtain is one function in order for it to be identified by another. The rest of the endowment as conceived by another may contain a sea of 0’s between or within the border enclosed by identified instances just so long as lines can be draw in order to see the extent to which that form of life obtains. It follows that a single line is just the difference between one identity and another. Identity projection is conditional, and since we can formalize the zero of a function, even if nothing appears, we are not licensed to deny subjectivity but only conclude that we do not have access to that form of life. This makes for a useful framework to consider theories of appropriation, as done below.Vertically, we can surmise point-wise identities between operations and the functions they obtain. Output is normalized—recall our Boolean-operator above—for what matters for identity ascription is not how it was produced but what was projected. Volume being in excess of an identified surface area follows from the consideration that to determine one's surface area ( = surface-level expression) within a singular context, the totality of that form of life entails a function proposing an identity between the nth function of n with a recursive function producing instances of n. As such, a totalizing function will never show up on that list. This is called diagonalization. It follows that a form of life cannot produce an expression that overdetermines all of its own possible expressions. If this cannot occur from within one's own form of life, what is identified as the form of life of another would only be valid within one plane. If a pair-wise identity projection is dependent upon certain conditions with respect to their form of life, then if the functional content of that projection in itself represents the zero of that function, then a form of life can harbor identities that are equivalent before projection but contradict after. To universalize the determinate of a form of life from one point may well end up self-refuting, but with interaction, what may be a single point allows one to turn an axis, revealing a web of connections between subjects’ expressions, present but not represented in that singular identity prior to interaction.So far, we have shown that a form of life produces models for interacting with the world from which these prototypes, or ways of inhabiting various conditions, can be tested, affirmed, or rejected. What if functions do not neatly line up with the indices of the scale organizing the space under consideration? We have to posit a bridge between the discrete and the continuous, between identity and subjectivity, explaining a point that continues unto another plane. If a form of life is continuous yet expressed by the function of an operation indexed to conditions in which that operation's output obtains or not with respect to others, we can look at those expressions as a series. If those points do not line up with the grid ( = reference frame) organizing a state of affairs, points considered as a function of coordinates between the integer scale on each axis allow us to enumerate irrational expressions that are nevertheless real. Irrational expressions are those whose functions do not neatly translate across forms of life. In fact, these are more closely related to the concept of the individual that we have been working through, for individuals are expressed by an operation. Irrationals are non-terminating; the functions by which they're expressed are formalized prior to a classified projection. What are termed irrationals in number theory are incommensurables in cultural study. It can be shown that they, nevertheless, have a logic to their construction. These functional indices represent a recursive operation indicative of the subjectivity of that individual more fundamentally. If an individual is not a static object, we can conceive of the arc of its mode of expression by way of that function's convergence or divergence from a discrete marker of identity.This method falls in line with our triangulation theory above, whereby the joint application of functions converging on a point can posit a measure of the extent to which forms of life interact. We can do this without having to render something static that is by definition a process. This reduction leads to the issues we alluded to above regarding universalization and diagonalization above. So these functions that do not quite match up with the frame organizing the space articulate a series that can be characterized as a never-ending sum of increasing or decreasing relations or ratios, for example, an expression given another that does not fully align with an identity marker and so produces another and another following a particular pattern. That encoded pattern is the logic or mode of expressing that incommensurable with a universalizing identity. From this, if we have two sequences from which we take the difference of corresponding relations in their enumerated order, and if that new series increases without limit, then the functions diverge. If they decrease toward a limit, they converge. Therefore, if two operations indexing the functional-content of expressions converge toward a third, then they converge toward each other. This means that we can spatially represent the extent to which functions from an endowment and between different forms of life interact without an identity having to be interchangeable across forms. Convergence, then, discloses an underling constructive continuum to these modes of expression.Our formalization of this point is key for a major question as of late in cultural studies that asks if it is possible, and if so, how and to what extent, for coalitions of signifying practice, here, modes of expression, to be built? Does our current state of affairs foreclose the possibility of not only affinities within forms of life but between them? (Wilderson 222–25). If a signifying practice can be formalized by a function within a plane organized along semantic and rhetorical axes, it appears that there is a model by which we can determine how and to what extent affinities and coalitions are possible. Recall that a function represents a relation between signified/signifier = concept/expression. As we can formalize how they come together, it appears that these interactions are possible insofar as a function converges or diverges from a rhetorical-figure/signifier (Gates 48). As functions are abstract objects in the sense defined above, a rhetorical-figure ( = objective-use) is the functional-content of an expression by which we can formalize and model specific operations within the domain under consideration. There is a reason why mathematician Tobias Dantzig, in his book Number: The Language of Science, entitled his treatment of this process the “Act of Becoming.” As the output of these compositions are dependent upon certain conditions, the above amounts to a spatial model in which the notion of a “collective improvisation” (Baraka, Blues People 26; Black Music 194–15, 203–04) can be conceived by way of functional composition and recursion.With that being said, I agree with Zora Neale Hurston's theory at the beginning of this paper, up to a point: Forms of life are like branches that “come round in queer ways.” But it appears that we can find the roots of these forms of life; it's just that they are ever shifting with numerous extensions as well as points of convergence or divergence. Roots must be conceived as branching connections, not origins. The issue is determining an origin and universalizing that over the domain, the seed being more than the tree rather than the other way, inevitably rendering movement to a singular point. Endowments’ objects are reflections of subjectivity from which that object can remake itself into a subject within the domains in which it participates (Gates 157). Our formalization of triangulation, a technique advocated by W. E. B. Du Bois, helps us analyze current issues within cultural studies as outlined above (Heesen et al. 3067–73). Issues regarding the joint application of different models within a form of life are cleared up by mapping these forms in-formation. Here, we posit a model in which affairs can be regional-specific and yet functionally related. A subject's operations appear different dependent across contexts, yet remains that subject with respect to the form of life from which it pulls to articulate an image of itself in those domains. These different images are functionally related.From our spatial framework, we now have a more rigorous conception of what constitutes a form of life. It is a space in which modes of expression function to articulate a particular worldview that is situated and whose form is based upon how it interacts with others within that space. These interactions can be modeled on operations over coordinates in this space that no longer have to render what that formation is to a single point that would make the map a point unto itself. However, we can account for how that form of life's shape evolves with respect to changes in its environment and the directions in which it moves. We find a more thoroughgoing definition of appropriation as well. We can actively model the extraction of a mode of expression from one form of life for use in another via a fixed-point that is considered representative of that life in total. Appropriation does this in such a way that it bars access to the output of that function to the ones that determined it in the first place. We understand via fixed-point theorems and functions of exchanging a point in one system for a system in total, that this process will always be incomplete (Gödel 193–98).Our formalization also reveals how we can show the vector of a movement without having to reduce it to a representative part that somehow references the whole. In this way, actualizing the future presently as what a movement is in itself makes sense—see Amiri Baraka on improvisation as praxis (Black Music; Blues People). A movement is a vector and representations only measure the rate of change at a certain point over their expressive arc from another's view. Within this model, the continuity of subjectivity can be formalized. A form of life is continuous at an identity that obtains within a particular domain if for each of its functions of expression, there is a domain such that for every expression, if its functional-content is within that domain, then the function of that expression is within that form of life. Much like the definition of limits in calculus, we find that a subject can participate in multiple contexts under various identities that are also considered functionally related within that form of life. Thus, each expression of a form of subjectivity appears appropriate to the conditions in which it participates, yet the various individuals who participate in that form of life are no longer mutually exclusive. To consider them so would be based on the limited access of those already in those conditions to the alternative identities under which others operate.Since we can enumerate these contexts by way of participation, that is, which operations are licensed or not given that form of life's environment, a spatial rather than linear conception of forms of life presents us with an alternative framework within cultural study. We can determine different forms of life insofar as certain properties of those operations obtain based on whether these operations are associative, commutative, or distributive. Affinities between forms of life are measured insofar as the expressions produced by these operations converge. Difference, then, by divergence. It follows that from any expression, one can abstract its functional content (Church 69–78, 168–76) in a manner relevant to the model they employ, for if there is an operation that produces that expression, the extent to which that function encodes a particular worldview and the success to which that model can be taken up for use by others can be measured (Kolmogorov 387–88). Thus, the usefulness given the complexity with which a particular expression becomes the basis for our ontology can be measured as well. These expressions encode a particular view of the state in which they operate. What is projected is decoded in a manner relevant to one's form of life (Hall 3–4). This is why a seemingly banal expression, when used in a particular domain, can be decoded in a manner that limits another's mode of expression in such a way that prejudices emerge. It was held by Rousseau in Origins of Inequality that language was a starting point at which relations of subordination and dominance emerged. Cedric Robinson connects translation and asymmetries in information to the advent of modern political-economic structures as well (14). Within this model, we conclude that expressions cite their enabling conditions. This context being a successor of the context marking an expression's initial use means that propositions are a map from that initial context over a range of context successors in which that projection can be determined appropriate or not. This logic models Alan Turing's Ordinal Logics explored below. Therefore, since we can model these operations, collectives are possible insofar as these operations can or cannot compose complex expressions, that is, collective improvisations (Baraka, Blues People 26; Black Music 194–95, 203–04).The ontology the above implies can be easily mapped onto a cultural studies example. Within that field, the pessimist argues that coalitions are impossible, for in order to obtain a coalition, one must be recognized, that is, identified, as a fixed-point within another's form of life. It is assumed that for black people, this is impossible, for they are already defined within all other forms of life as that which cannot obtain therein (Wilderson 222–25). The error in this reasoning can be seen from the model we developed above, for an identity as primary approach leaves out what animates that identity in the first place. Thus, the possibility of affinities between forms of life is not an identitarian one. Looking to operations first as that which composes identified positions whose functional content obtains a sense within the domains to which they are introduced, we can make sense of James Baldwin's claim that this error is instantiated so as to cover up a precarious fact (144). From an identitarian position, and by definition, whites cannot be “white,” for this very same operation diverges from what it requires to substantiate its own position. It diverges, for it defines the other as that which cannot obtain in the system it employs while citing resources ( = origins) from outside the system. Consider when “white” light is shined through some medium, it is revealed as being composed of different colors, making white a non-color color in itself. Wittgenstein would remark that white, then, could not be a color after all. What we know as “white light” is a retrospective determination of what existed prior to being sorted by that medium. White may have semantic content for, info-theoretically, we can ask “What is white?,” but we have to refer to the frame or medium by which we made the query and by which divisions were made sense of retrospectively, making the predetermination “white” the framing medium, not an entity in the domain it organizes. Thus, what “white” is is not really informative for information = (query + answer)—see Floridi's introduction on information theory. Consequently, we can conceptualize what “white” is but its verifiability is had by what it denies on its own terms, providing no way to parse the data on white-ness for its very assertion denies value to what substantiates it.However, blackness can be known under different names that can be seen as functionally equivalent, connecting their contexts of assertion so that we see that they converge but don't come to a single point. Our concept for the color black absorbs all colors and therefore is where they all come to reside. Thus, these forms of life are continuous despite being known under superficially discrete identities. As such, we do not need to show a one-to-one link between all possible forms of expression and one identity; we only need to formalize what that movement is. With blackness being an already integrated concept, we need to study what compositionality entails. In so doing, we formulate different forms of life that do not have to be centered on one point. Therefore, blackness, as a global concept, is not spread so thin as to dissolve it of its significance within the contexts in which it appears.We move, then, from a rationalist/idealist ontology in reaction to an ontology grounded in physicalism/materialism to an interactionist framework. What is good from rationalist and materialist strains posits the two as being different characterizations over the same issue. Their division from their own perspectives was presupposed but unaccounted for in the systems they founded. A traditional materialism comes from an
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