Precursor Article to “Networkologies”: “On The Metaphysics and Physics of the Networkological Endeavor” published in ‘Speculations: A Journal of Speculative Realism’

[Note to the Reader: Here is the full text of the article published in Speculations: The Journal of Speculative Realism, Vol. 2.

Some precursor segments of Networkologies (Zer0, 2014) were published as the work was in progress in two installments in Speculations: A Journal of Speculative Realism, Vols. 1 & 2. Links to the issues of Speculations, see here and here. Due to formatting issues, the first article is best accessed via pdf here. The articles do not need to be read in sequence, as they cover different issues. This first article is a general introduction to networks and their relation to philosophy. Much of this has been reworked in the final manuscript.

The second, more recent describes the metaphysical core of the networkological enterprise, as well as some of the applications to the physical world. For the page on this website with the entire text, see here. Additional excerpts of the work in progress were posted on this blog as regular posts, including here (on Networks and Emergence), here (on Networks and Complexity), here (on Networks and Extimacy), and here (On Networks and Parameters).

The first section of this article describes the metaphysical core of the networkological endeavor. This is done by means of an articulation of the concept of the network diagram. This concept is composed of four primary elements, namely, the node, link, ground, and network/level, each of which is described in turn.

The second section of this article then goes on to begin to describe how a networkological approach can begin to be applied to some of the traditional notions of the physical world, such as matter, mind, space, time, extension, reality, knowledge, etc. This section will be reworked for the second volume of Networkologies, the draft of which this is currently a part.]

On the Metaphysics and Physics of the Networkological Endeavor: An Introduction

[diagrammatology: the network diagram]

ELEMENTS. The networkological project is an attempt to develop the potentials implicit in network diagrams, and in relation to networks in the wider world. Network diagrams are iconic signs whose relational form resonates, in varying degrees, with relational forms in networks in the world. The philosophical concept abstracted from the multiplicity of networks and network diagrams in the world is known as the network diagram. The three primary components, or elements, of the network diagram are the node, or individual, the link, or relation, and the ground, or context, from which these emerge. In addition, when a group of network elements are contained by other network elements, we see the manner in which what is considered an element of a network can also be a network as a whole in its own right. When network elements contain each other in this manner, we say that there is a difference in level of scale between the elements and whole network(s) in question. As far as we know about the structure of our universe, all networks are elements and all elements networks, depending on the level of scale, all the way up and down, up to and potentially including the open, at both the smallest and largest, most concrete and most abstract levels of scale. In this sense, we can say that the network diagram has three primary elements, namely, the node, link, and ground, as well as a supplementary element, which can be called the network, as a whole, or the level of scale, depending on one’s perspective. The network diagram thus takes the form of what will later be described in depth as a triandic structure, one inherent to the manner in which the oneand manifests in the threeand, as described by the concepts of the node, link, ground, and network/level. Networks elements arise in many forms in the world. When a node emerges from a ground, we say that it has individuated, and when a link emerges between nodes, it has connected them. Levels emerge within networks by means of the process of leveling, and grounds may give rise to or absorb any and/or all of these elements. Networks/levels, nodes, links, and grounds may be static or dynamic, heterogeneous or homogeneous. Nodes may encompass all of an element, or only an aspect thereof. Links may be uni-, bi-, or multi- directional, precise or fuzzy (indicative of what Ludwig Wittgenstein would call a ‘family resemblance’), single or multi-threaded, etc. Grounds may also be homo or hetero-geneous, flowing or static, and levels may take in groups of network elements or whole networks, may fold in various ways, etc. Networks include any and all of these permutations. From the diagrammatic germ described in this section—the threeandic formation of the node, link, ground (and level)—the entire networkological project springs.

DIAGRAM. The concept of the network diagram, and its associated concepts of network elements, are abstractions from networks in the world, and represent the networkological endeavor in its most abstract form. The concepts in question are clearly abstractions, and they collapse under the weight of this abstraction when taken to their extremes. However, as the source of generalization, abstraction has its uses, in that it can help us clarify in extreme form aspects of more concrete formations in the world. The first and foundational concept of networkological diagrammatology is that of the network diagram itself. The network diagram is both a concept and a diagram, for it is a concept of a sign, and the sign of a concept. A diagram is a sign which represents a concept, but the network diagram is a diagram which represents a concept which is also a sign. For unlike signs such as alphabetic or ideographic signs, network diagrams both say and show, they represent and perform relation. It is for this reason that the network diagram is both sign and concept, and while it cannot be easily drawn, for it is the concept of the network in its most abstract sense, and thus, abstracted from any particular form thereof, it can be described by means of the articulation of the relations between its component concepts.

NODE. The concept of the node in the network diagram represents the principle of unity. At a given level of scale within the network diagram, a node is without parts, completely identical to other nodes in the network, for in fact, each node is simply an instantiation, an ingression, of the node which is itself a concept within the concept known as the network diagram. It must be kept in mind, however, that no node can be a true unity, for true unity is an abstraction, for it would be without relation, and hence, we could have no experience of it. For this reason, we can say that the concept of the node is a form of unity- within-difference, or the one(and).

LINK. The concept of the link in the network diagram represents the principle of difference. Links hold apart that which they connect, and this is what is meant by difference, namely, disjunct-unity, or the two(and). When the concept of the link intersects that of the node, the result is the plurification of the node into nodes, for once there is a link, there are necessarily nodes rather than a node, and hence, a network rather than simply an element.

GROUND. The concept of the ground in the network diagram represents the principle of indistinction. Grounds are neither/nor, for they are neither fully inside a network nor outside of it, and in this sense, we can say that they are extimate to networks. This is not the only manner in which grounds are neither/nor, however, for they are also neither unified nor dispersed, neither nodes nor links, and while they may be the background of a network, depending on how that network is deployed in the world, they may also be the foreground. In the capacity of foreground, a ground functions as a node, just as when it functions as a background, the ground functions as a link, in that it links the network to the wider world. When the concept of the ground intersects with that of the node and the link, the result is the potential for change within the network articulated by the node and the link. Change always involves production or consumption, which are forms of transformation. For when nodes and links change, they do so by drawing upon the ground, or releasing into the ground, that which is produced or consumed in order to make this change occur. Some change may even lead to the emergence or dissolution of individual nodes or links. The concept of the ground deepens the difference presented by the concept of the link, developing disjunct- unity into self-differing, or the three(and), for it is by means of the interplay between nodes and links with the ground that networks can become different from themselves. Furthermore, grounds exist both inside and outside a given network, and in this sense, they allow the network to relate to the wider world. In this sense, we say that grounds are extimate (exterior yet intimate) to the networks of which they are a part. While links and nodes may exist in many networks at once, only grounds may be shared by networks, and in this sense, exist neither solely in one network nor another. And in this manner, we see how the neither/nor of the ground has the potential to deepen into the both/and of the level.

NETWORK/LEVEL. The concept of the network in the network diagram represents the principle of emergence, and for that reason this concept is doubled, for it is both the network as a whole, and the level as a part of another network as another whole. In this sense, we see the manner in which the notion of the network/level deepens the disjunct-unity of the link and the self-differing of the neither/nor of the ground into the emergence, or threeand, characteristic of the both/and of the network/ level. The concept of the network/level is both whole and part, it contains itself, and does so infinitely, and with infinite intensity. When the concept of the network/ level intersects with that of the node, level, and ground, it causes them to enter into a state of emergence. Such a state is doubly split, for emergence at any level implies a relation to a macro level which contains the level in question, and a micro level which is contained therein, thereby giving rise, in their intersection, to the meso level which unites them. Hence we see the split between meso- macro and meso-micro, as well as that between meso and macro-micro, which itself splits amongst itself, taking on thereby the form of a threeand. This self-containing threeand (split macro-micro, split between meso and macro-micro, split between meso-macro and meso- micro) has a form which mirrors the manner in which the network diagram can be considered as itself split between a threeand in which diversity contains unity (the level which contains the ground, link, node, and network), and one in which unity contains diversity (the network which contains the node, level, ground, and level). When the concept of the network/level intersects with the concept of the node, it transforms the pure unity of the node within itself, the lack of distinction between that which it unifies, into a disjunt-unity in which distinctions of various sorts may occur. When the concept of the network/level intersects with that of the link, the disjunct unity between nodes is transformed such that the relation between any network elements and/or networks can be seen as a form of link, thereby expanding the disjunct-unity of the link between self-differing and emergence. And when the concept of the network/level intersects with that of the ground, it transforms the self-differing of the ground into an emergence, in that any individuation, decomposition, and/or transformation of a network element in relation to a ground becomes the potential for an emergence of a network/level as well. However, the self-differing of the ground is also that which transforms the concept of the network into that of an emergence, or that of a level, for it is the self-differing of the concept of the ground which, as self-exceeding, pushes the concept of the network into the emergence of the level. The ground represents that which, as both inside and outside the network, exceeds it, and it is for this reason that the self-exceeding aspects of the network diagram, the –andic side which it bring to the three, is split between the concept of the ground and that of the network/level, while also finding itself in germ in the notion of the disjunct-unity within the concept of the link. The result is that disjunct-unity, self- differing, emergence and unity are necessarily various sides of the same, in that unity-in-difference, disjunct- unity, and self-differing, are all ultimately aspects of the manner in which the world emerges from within itself. While each emphasizes different aspects thereof, they are nevertheless all abstractions from the self-differing emergence of what is. And while emergence emphasizes levels, self-differing emphasizes grounds, and disjunct-union emphasizes links, and unity-in-difference emphasizes nodes, ultimately, these are all but sides of the oneand as it brings itself forth. Levels link networks, and are networks, for they allow for each network element to function as each other, depending on how they are related to other networks. That is, levels may link nodes and nodes, links and links, grounds and grounds, networks and networks, as well as any combination thereof. These structures, as described above, continue all the way down in networks in the world, at all levels of scale, and do so fractally. That is, the concept of the level describes the manner in which the oneandic nature of emergence manifests itself triandically, that is, as a fractal and holographic oneandic proliferation of threeands within threeands, at all levels of scale. The concept of the network/level show us the manner in which the concept of the network diagram describes the concept of relation, for it intertwines that of unity, disjunct-unity, self-differing, and emergence, thereby producing intertwined series of triands which give rise to the fractal, holographic, relational complexity of all that is.

THE ONEAND. By means of the relative degrees of reification of the oneand, as manifested in unity-in- difference, disjunct-unity, self-differing, and emergence, the oneand comes to emerge from within itself. It thereby produces relation, for it is relation in the process of its coming to be. And to the extent to which we can say that the degree of reification manifested by unity-in-difference is the most extreme present within the network diagram, we can say that the oneand in this guise cloaks itself, and does so in a manner which can be described as that of the one(and). The movement from oneand to one(and), then, describes the motion of the concept of the network diagram within itself. In addition, we can also say then that the concept of the link represents the notion of the two(and) (as well as the intermediate form of the self- exceeding binary of the twoand, as utilized by figures such as Bergson, Derrida, Luhman, Deleuze, etc.). And beyond this, the concept of the ground represents the notion of the three(and), and the level that of the threeand which opens onto the oneand itself. For it is by means of the plurivocity of the level, of the production of differences in kind from differences in degree, the movement from the indisctinction of the ground to the multiplicitous distinction of the level, that we see the emergence of the new within emergence itself, the production of the actual from within the potential. This process, which continually produces itself from itself, describes the manner in which the threeand manifests the oneand. For while the threeand is a concept extracted from a diagram, that is, a representation of aspects of the world, the oneand is the world, it is the world and the concept thereof, it is the process of the world in its self-exceeding, and the threeand is merely the means whereby it comes to know itself as relation, fractally, holographically, and immanently, at all levels of scale. All of what follows is simply a wager on the potential resonance between the concepts presented here and the wider world, such that the articulation of what follows is simply an unfolding into actuality of the potentials abstracted by the threeand of the diagram from its relation to the world, a process which must now effectively be reversed.

[matrixology: extension, self-differing, and worlding]

MATRIX. Matrixology is the study of how networks manifest in the world of experience. As a philosophy of relation, the networkological approach does not firmly separate ontology from epistemology, matter from mind. Following Baruch Spinoza, the networkological perspective grounds all that is in a single fundament, of which matter and mind are simply aspects. This fundament is called the oneand, or matrix, for it is within all, as well as that which gives rise to all, it is the emergent self-differing which gives rise to all existents. All forms of matter and mind are so many various incarnations of matrix, and matrix is within all of these and beyond them all. Matrix is the potential to be of all that is, as well as what potential becomes as it unfolds into the actual. When matrix has not come to be it is called potential, when it comes to actualize itself in a location it is called matter, and when matrix comes to experience itself, it is called mind. Mind and matter co-permeate, if at differing degrees of intensity and in different forms, at all levels of scale. For the networkological approach, and unlike the inheritors of René Descartes and Immanuel Kant, mind is not the exclusive province of humans or even animals, but something which ‘goes all the way down’ to the quantum level and potentially beyond. Unlike those who rigidly bifurcate the world into mind and matter, or subject and object, the networkological approach does not need to bridge a mind/body gap, for it sees none. Rather, its task is to explain the diversity of combinations of matter and mind that give rise to the varied phenomena in the world. Within matrix, there are several aspects of the oneand which manifest as the open, that is, as that which prevents matrix from ever being fully at one with itself, and whose avatars structure its modes of appearance, or matrixology, thereby giving rise to variety in the world. From an epistemological perspective, the open manifests itself as the undecideability of the fundamental obstacle in its varied forms. From an ontological perspective, the open takes the form of originary potential. And from the ethical point of view, the open takes the form of the call to maximum robustness. While these sides all present themselves, and will be explained in turn, they are all refractions of the same fundament, namely, the oneand of matrix in its process of emergent self-differing. The networkological approach, which frames itself relationally at the intersection difference and relation at the site of emergence, is thus ultimately neither a philosophy of ‘the One’ or ‘the Two’ but the one which exceeds itself, the one-and. Thus, it finds common ground with any approach to entities which finds them in the process of emergent self-differing, or becoming-other, for this is the necessary fundament for any truly relational philosophy. In the what that follows, the manner in which matter and mind intertwine within matrix as experience will be examined, first in its most general and abstract sense, and from there, in the varying ways in which forms of matrix emerge from one another, from the simplest to most complex. This examination of the ways in which matrix exceeds itself is what is what the networkological project calls matrixology.

EXTENSION. As matrix comes to be, it differentiates. While such differentiations may be stacked on top of each other in superposition, when matrix comes to be, it does so in ways that allows for differences which exclude each other. The result is an exclusive relation of a particular difference to matrix, segementing it and extending it within itself, producing spacing or distance within matrix, resulting in the genesis of separations, disjunctions, actualiztaion, and change. Such a process describes the manner in which matrix gives rise to the distribution of perspectives on what exists. Each perspective entails a view of the whole, one which emphasizes certain aspects over others, and this is what is meant by location. Each location is a node which links together the varied changing inputs of all that is, and perspective is the name given to the manner in which the location of an entity within an extended network determines, in relation to the nature of the entities in question, the strength of the impact of each on the other based influence based on the relative degree of separation between them. The emergent self-differing of matrix into localized perspectives is the result of the process whereby matrix comes to actualization, for it is only by means of this separation and self-distinction that matrix is able to localize, differentiate, experience itself, and appear to itself, and ultimately, these are various sides of the same. Most theorists today believe that our common universal matrix, or universe, originated within a singular formation often simply called ‘the big bang’ or ‘the singularity’. This originary matrix, from which all in our universe came to be, began at some point to self-differ, to shift from potentiality to increasingly complex forms of actualization. This process allowed for the growth within itself of what, following Whitehead, is called extension, namely, the opening within originary matrix that produces localization, perspective, and the relative mappings of changes therein, known as spacetime. Extension, spacetime, localization, and perspective are simply so many different ways of saying that the potentiality of the originary matrix began at some point to actualize, that is, to exclusively differentiate, and unfold into what we experience. Because our language is itself the product of an extended universe, it is ill equiped to describe the process of the coming to be of coming to be, of the genesis spacetime, unfolding, extension, actualization, etc., and it is for this reason that any attempt to do so must always use language against itself, fold back upon itself, etc. We can, however, describe this state at least negatively, and in relation to certain phenomena that exceed standard extended formations in our current context. At its furthest extent, we call all that we can experience, to the limits of our current spacetime horizon, the universe. However, the universe may also be part of a set of universes, or multiverse, which exist within a larger overall context, known as a megaverse. All of these are developments of the originary matrix which formed all of the current context within which we exist.

SPACETIME. Since the structure of spacetime networks differ according to the perspective of varied locations within the universe, there is a difference between what, following relativity theory, is called the proper time of an entity, that is, the experience of change as measured from the perspective of any given entity, while the change in time for a given entity as measured from the outside will be called a temporal mapping. Both of these are different, however, from the change of the universe as a whole, the ordering of which may be widely spatio- temporally different according to differing perspectives on the universe, and that from which all proper times, even if incompossible, emerge. Following Whitehead, we call this overall change, that from which proper times emerge, the creative advance of the universe. Building upon the distinction between proper time and creative advance, it is also worth conceptualizing the distinction between space as it is apprehended from a given location (called an inertial frame in relativity theory), and that as mapped from an outside location. We will call the first an entity’s proper space, and the apprehension of a space from an exterior location a spatial mapping. Space and time are ultimately abstractions, for it always takes time to move in space, and the changes which we use to apprehend movement can only be apprehended by motion in space. Even in everyday language, we say a voyage by car to another city is ‘an hour away,’ and we use the movement of a hand on an analog clock to describe changes in time. For this reason, the networkological project will generally speak of spacetime locations, rather than moments in time or locations in space. According to the theory of relativity, when one moves through spacetime, no matter how curved that spacetime may be, one’s own spacetime always seems flat, it is only that around one which seems curved. For in fact, only if one moves within flat, non-warped spacetime will one percieve the spacetime of its world not warp around it as its move. We will speak of an entity’s proper spacetime as the apprehension of time and space from path within spacetime of that entity, while the apprehension of spacetime from an exterior location will be called a spacetime mapping. Distortions in spacetime are never experienced directly, but only indirectly as one changes location in spacetime (which includes remaining in one location while the world around you changes, or moving in space while the world around you changes). This is because change is always relative (that is, any inertial frame of reference is equivalent to all others in relation to the laws of physics), and hence any entity can only experience changes in its own spacetime curvature indirectly by apprehending changes in the world beyond it.

POTENTIAL. All matrix has within it the potential for self-differing. Potential is emergence under the aspect of the future in the past (emergence that will have occurred), while the actual is emergence under the form of the past in the future (emergence which is always already different from what it was). From originary matrix to any bit of matter within the world, it is fundamentally unknowable whether the potential to be different present in any actualization is the result of mind or matter, or due to internal or external causes at a given localization in spacetime or level of scale. Some of the reasons for this are simply practical ramifications of the manner in which extension intertwines matrix within itself. It is logistically impossible to observe an entity from all spacetime locations, and at all levels of scale, and hence to know all the influences upon a matter, as well as all the hidden potentials therein in the future. What’s more, it is impossible to observe a matter from within, and thereby know the degree to which its decisions come from its form of filtering its influences, those influences itself, or some other, more fundamental source of differing such as originary potential. But to know another matter from within in this manner would be possible only by means of being that matter, which violates the very notion of matter itself. Beyond this, however, there is the issue of quantum fluctuations which, under the correct circumstances, could cascade up the series of networks in a given matter and tip the scales of a decision towards a given outcome. Researchers are relatively convinced of the fact that is impossible to know if, on a quantum level or below, there is some aspect of what is which renders matter itself fundamentally indeterminate. Within quantum mechanics, researchers still debate whether or not the fundamental indeterminacy of quantum fluctuations is due to the influence of minute shifts within the context of the quantum event in question, conveyed in a manner which is too delicate for our instruments to detect, or whether these fluctuations are the result of something present within the particles and sub-matters in question. Beyond this, there is no way to know, at least within contemporary science, whether or not there might not be influences which we simply cannot sense, which come from beyond the confines of our universe, simply because the universe is the horizon of our current experience. For all of these reasons, it makes sense to acknowledge the fact that all matrix has the power to surprise us, for in fact it has never ceased to do so. While it may behave in regular ways for the most part, it seems as if there is almost an inverse ratio between the level of precision with which we need to know it, and the degree to which we can know it. Let it suffice to say that we can understand matrix, particularly in general, but that in particular, it is nearly impossible to know, and we can call this impediment to knowledge, and the difficulties it gives rise to, the quandary of potential. And in the right conditions, all that we know can be given rise to by matrix no different than what we see before us in our everyday lives. All that is, or could be, exists as potential within any and all. The capacity for self-differing, in all its forms, is what is known by potential, and all matrix has this within it.

SELF-DIFFERING. For the networkological endeavor, matter is that within matrix which is able to actualize a difference, and mind is that within matrix which is able to experience difference as potential which it can then bring to actuality via action. When matrix is delocalized, however, it is pure potential. But as matrix comes to actualize itself, it comes to differ with itself, not merely potentially, but concretely, exclusively in relation to a location, and hence, actually, giving rise to both difference within matter, which is then experienced by mind, as well as difference experienced by mind and then actualized within matter. Mind and matter are the two aspects of matrix which allow this transition, this emergence, to occur. As a philosophy of relation-in-process, the networkological perspective does not fundamentally distinguish epistemology and ontology, subject and object, mind and matter, nor does it distinguish whether difference originates in the matter or mind sides of matrix. Matrix differentiates into matter and mind simultaneously as potential comes to actuality. Mind is the capacity within matrix to be affected by difference, just as matter is the capacity to be difference, and subjectivity and objectivity are, within conscious minds, simply higher-level echoes thereof. To ask which precedes or grounds the other is a false question, for matrix gives rise to these very distinctions in its coming to be (and later in this work, we will describe this false question by means of the notion of the obstacle of experience). All matrix has potential for self-differing, just as all matter has potential to be differently, and mind to experience differently. Self- differing, extension, and experience are three sides of the same manner in which matrix emerges from itself, grasping itself as experience, and giving rise to appearance from within itself.

DISTINCTION. Within the self-differing emergent extension of what is, stasis interpenetrates with change, and continuity with discontinuity. Extension gives rise to both differences in degree, or intension, and differences in kind, or emergence. Emergence, occurs when intensive differentiation differs with itself or the world around it. The result is that discontinuities arise in terms of space, time, matter, and mind, giving rise to analog/ continuous differences of degree, and digital/distinct/ discrete/discontinuous differences of kind. Were there no discontinuities, change would be limited in the extent that it could develop, and likewise, were there no continuities, there would be no opportunity for entities to interact and change thereby.

MIND. At a given level, any material entity or system has a series of inputs which affect it, from both micro-/ interior (sub-matters) and macro-/exterior levels of scale, and these then must be converted by the matter in question into actions. Mind is that which feels the influences upon it a given matter, experiences them, and then decides upon these influences, in light of its relevant potentials, by executing an action within its own matter. It must not be thought that mind is a magical substance that somehow inhabits matter in a ghostely manner. Rather, it is simply the manner in which matter relates to itself within experience. Mind can be thought of as the giant distributed thinking present within the brain of the universe of matter. Put differently, mind is that which processes the micro- and macro-level inputs within a matter, in light of the potentials relevant to that matter at its level of scale. That is, mind is the manner in which the micro folds into the macro, and the macro into the micro, at the level of the meso, and in relation to the potentials within that meso itself. This folding, beyond the three-dimesions of space and one of time, occurs in what can be thought of as a sort of fifth dimension material, that of mind. In this sense we can think of the intertwining of mind and matter, experience and action, macro and micro, as similar to a non-orientable twist within topological figures such as a cross-cap or Klein bottle. For there is no way that micro and macro levels of spacetime could intertwine within a meso-level of matter without in fact turning space inside out at the level of the meso, and mind is precisely this turning inside out of matter within itself, a doubling of matter which is yet still nothing but the same. Where is mind located? Perhaps this is a false question, for we live not in a world of matter, but of matrix, of which matter is simply one side, and one we only know indirectly through the experience provided by mind. However, in relation to that material side of what is, we can say that mind is both as if it were on the same level as matter, but also as if it were in a sense dimensionally orthogonal to it. Matrix is both mind and matter, and these can be thought of as two levels of matrix, but levels which do not relate to each other as macro and micro, but as meso to meso in different yet intertwined domains. That is, like the manner in which electrical and magnetic waves in the physical world are two sides of the same electromagnetic wave, but on different yet intertwined dimensional planes, so mind and matter are like two side of the same, on diferent yet intertwined planes. One is the plane of experience, or mind, the other the plane of action, or matter. However, while electromagnetic waves are one step out of phase with each other, changes within mind and matter remain in phase with each other. This is the sense in which mind is an interiority to matter, and yet, nothing but another aspect of that matter itself, for in fact, mind and matter are simply two sides of matrix, two sides of the same. Mind is what casts matter outside of itself, into the world of influence and experience, just as matter is that which localizes mind in the here and now of action. If energy is the potential within matter to configure itself differently, then mind is the potential within matter to understand itself, to split itself up and re-relate to itself based on differences in location within extension. While matter and energy are strictly convertible within physics, as two different forms of the same thing, mind can be thought of as matter to a higher power, an intensification of matter which is a difference in both degree and kind, even as it is simply nothing more than that matter itself under another aspect, a twist of matter within itself, in a sense. Likewise, the reverse can be thought of mind to a higher power, a concretization and actualization within localized extension, wrenching the plenum of influences into the here and now of action. This snake eating its own tail is matrix, and matter and mind are two sides of the snake, each turning themselves inside out within each other, two sides of the same.

WORLDS. Matrix, mind, and matter divide and link up to locations within extension according to networks of symmetry within the manner in which potential actualizes within what is. The result is that matrix differentiates, giving rise, along with spacetime, location, and perspective, to particular matrixal entities. Each of these entities has a matter side, known as ‘a’ matter, and a mind side, known as ‘a’ mind. Each side, in its way, is the condensation and/ or expansion of the other, each in its way, even as each is also the condensation and/or expansion of the whole, each in its way. That is, location, spacetime, matter, mind, extension, differentiation, and experience, actualization, and potential are all so many sides of the same process whereby matrix comes to emerge from itself. When mind is localized as ‘a’ mind by means of ‘a’ given matter, it takes up a particular position within spacetime, producing a unified perspective on what exists, and what this unified perspective presents to that mind is that mind’s world. Each world is a recasting and reworking of all that is into the graded series of appearances, the strength and positions of which is determined by the structure of spactime and the nature of the matters of both the mind in question the matrixal entities which form its contexts. Any given world indicates the manner in which the world appears to a matrixal entity composed of the matter, mind, and location in question. For self-conscious and conscious organisms, the world appears consciously via perception, but for simpler entities, the world is still experienced, but not in a manner which is conscious. Thus, while simple entities certainly have a world which appears to them, they cannot be said to know this, but only experience it. At all levels, a mind’s world is continually recreated as the context around that mind shifts.

WORLDASPECTS. The myriad of worlds or graspings of the world form aggregates and subaspects in a variety of ways. The combinations or sections of these give rise to aspects of the appearance of the world, known as worldaspects. There are varying types of worldaspects, suchasastatic/0-dimensionalworldpoint,a1-dimensional worldline, a 2-dimensional worldsheet, a 3-dimensional worldsolid, and a 4-dimensional worldhypersolid. A world is an intertwining of any or all of these into a complex and shifting whole. All worlds are the result of the manner in which matrix experiences or grasps itself, giving rise to experience as appearance by means of the process of self- grasping in self-differing known as worlding. If extension indicates the manner in which matrix differentiates, worlding is the manner in which matrix reconnects with itself in difference at higher and more abstract levels of emergence. Ultimately, we cannot know whether or not the manner in which a mind experiences its world corresonds to ‘what really is,’ for the world is never experienced in this manner, but only by given minds from given perspectives. In this sense, there is no ‘what really is.’ What’s more, it is impossible for any given mind to determine the degree to which what they experience is due to its own nature and location, or that of its contexts. This will later be described as the obstacle of experience. What there is, however, is intertwined series of worlds, and varying degrees in which these resonate with each other.

WORLDEVENTS. Each time a given mind or matter changes, this is known as an event. Any event always occurs in a given world, and as such, is a type of dynamic worldaspect which is also known as a worldevent. There are three varieties of worldevents which can be experienced by a given mind in relation to its world, namely, interior material events, exterior material events, and interior mental events. When a mind experiences an interior material event in its world, such an event is experienced as a shift within the sub-matters of the matter relevant to the mind in question. For example, when I say, “I’m hungry,” I say this because one of my sub-matters, namely, my stomach, has communicated to my consciousness the sensations associated with lack of food. An exterior material event occurs, however, when matters outside the matrixal entity in question change. For example, when I say “The kettle is boiling,” I am recognizing a shift in the matters outside of me. An interior mental event, however, cannot be known by any mind directly, but only indirectly, through a loop through other matters which are then experienced by the mind in question. For example, when I move my arm, the aspect of my mind that moves my arm does not experience this as an influence coming from outside it, simply because it is this. It can experience the movement of this arm afterwards, however, indirectly, by experiencing the sub- matters in question moving. Minds cannot experience themselves changing except by means of a loop through either interior or exterior matters. It is in this way that some complex organisms have developed special loops within their control systems, or brains, such that some aspect of the brains in question are there specifically to experience others, thereby giving rise to what is called ‘self-consciousness.’ Since the mind of any given matrixal entity is merely a processor of influences and actions at a higher level of scale, it cannot experience itself but indirectly, after a delay and by means of its effects. And while I have used examples above to describe this mechanism by means of conscious entities, the same can be said, in much simpler fashion, for simple entities which do not percieve the world, but are only affected by it. Thus, when a stone breaks, we see a cascade of internal material events that give rise to a set of influences on the matter of the stone. These are processed by the mind of the stone, which gives rise to an internal mental event, which manifests itself in the matter of the stone as a particular type of break. This break is experienced by the mind of the stone indirectly, by means of a shift in the influences of its sub-matters and exterior matters, for the matter of the stone is in many senses nothing more than the intertwining of these two levels within a given spacetime location. After the stone breaks, however, can we speak of the stone as a single matrixal entity, or rather, one which is now split or dispersed? These sorts of questions depend upon the networks of reference which are applied to the matrix in question, and this depends upon the manner in which the entity in question is apprehended a given entity. While it may be possible to say the stone now becomes a dispersed entity, or rather, multiple smaller entities, this all depends upon the manner in which the matrix involved is divided up into networks within the world of a matrixal entity which does the apprehending of such a split. There are, however, many dispersed matters in the world, with dispersed mental aspects, and they simply function differently than unified matters and minds. Since ultimately all matters and minds are divisions of matter and mind, just as all matrixal entities are divisions of matrix, the question is not whether or not a given division of the world into aspects and events is correct, but rather, what networks of reference and perspective is implied by a given division. For the networkological project, all divisions of matrix are possible, and no division is truer than any other, for any given division of matter, mind, and matrix into aspects is symptomatic and provisional, rather than ultimate. Aspects and events are simply aspects of all that is.

WORLDING. Worldaspects and worldevents may conjoin to create the larger entities of which a world are composed. When events line up in a series, generally, though not necessarily, due to the unifying aspects of a single spacetime location or a given entity, the world aspect this gives rise to is known as a worldline. Worldlines, like all worldaspects, can be disjunct or unified. For example, the series of American presidential elections gives rise to a disjunct worldline. A unified worldline is one which describes the appearance of continuity between the events in question. When such a continuity is seen from inside, this is known as an interior continuous worldline, and when seen from without, an exterior continuous worldline. A continuous interior worldline is known as a duration. Any interior worldline has a shifting dynamic context which corresponds to it, the inverse of that worldline, the aggregate of the worldslices which correspond to the interior events of which that interior worldline is composed. This inverted line is known as that worldline’s interior worldstructure. Each interior worldline may be complemented by a variety of exterior worldlines, which may not correspond in all degrees with that of the interior worldline. The same disjunct unity described here in regard to events and worldlines, can be seen at higher levels of scale in regard to worldsolids, worldhypersolids, etc. Each worldaspect may be unified or disjunct, has interior and exterior sides, has inverses, and is composed of sub-worldaspects and is part of aggregate worldaspects at higher levels of scale. Appearance occurs to minds via the intertwined worlds which matters give rise to. Worldaspects are fundamentally related to spacetime networks, for spacetime is itself simply an abstraction of the aspects of worldaspects which have to do with location within the shifting dynamics of the world.

REALITIES. Each matrixal entity has its own world, and each event shifts worldaspects in relation thereto. No world exists in isolation, however. When minds share a given context, physical or otherwise, they are likely to have strong similarities between the form of their worlds. Whenever there are multiple worlds layered on top of each other in this manner, the resulting network of worlds is known as a pluriverse. When a pluriverse is constructed by matters which share the same general spacetime context, we say that this pluriverse is a physically localized material pluriverse. Within any set of minds within a spacetime context, the zones of symmetry between their worlds give rise to what is known as a shared world, or reality. Any reality is dependent upon the minds which exist in it, and its parameters are set by the interaction between them and their contexts. Realities can be physical or mental, for the same strutural parameters apply, namely, the establishment of shared points of reference within conditions of flux. Worlds come in nested networks, while realities also come in nested networks, but also in varying degrees of fuzziness, and in varying forms of complexity, as determined by the worlds of which they are composed. The degree of fuzziness of a reality is indicated by the degree of asymmetry it contains. The higher the degree of asymmetry, the less the entities which compose this reality will be affected similarly by events which appear to them in their worlds, and therefore, it will be difficult for any sort of order or complexity to form. Some degree of symmetry within the basic reality shared by a group of entities is needed if order and complexity of any sort can emerge. For conscious organisms, the reality they share with other entities in their world must have relatively high degrees of symmetry for them to operate within that world in a manner which can support cause and effect in regard to their action, support learning, etc. Thus, there must not only be a relatively high degree of symmetry in regard to space, but also a very particular sort of asymmetry, known as directionality or the arrow of time, in which time moves in only one direction within its spacetime contexts. Such a condition is also necessary for the development of complexity, life, and other preconditions of consciousness. For self-conscious minds, the same requirements hold, if at higher levels of complexity.

REALITYASPECTS. Realities describe the the intertwining of worlds via matter and minds, such that realities are composites of the worlds they contain, in which the incompossible aspects of these worlds are recast as excesses which are fuzzily and extimately included within this reality. Realities, like worlds, can be divided into events, lines, sheets, solids, and contexts/structures of various sorts and degrees of complexity. The difference between them, however, is that worlds are inherently divided between interior and exterior sides, while a reality is always shared between entities, and emerges from the intertwining of interior and exterior world aspects. As such, there are internal and external sides of every entity and event, but no direct experience of mind enters into realities, where this does occur within worlds. This disjunction between world and reality is manifested as what will later be described as the obstacle of privacy, namely, the inability of one mind to experience what it is like inside another.

REALITYFORMING. How many worlds and realities are there? Ultimately, there are as many worlds as there are entities and events (which in their way are two sides of the same), and as many realities as there are networks of worlds. Just as worlds are networks, so are realities networks composed thereof, if differently. And in fact, all worlds are composed of realities, and all realities composed of worlds, down to and potentially including the quantum scale (where such distinctions become fuzzy), and it is the mind of a given matter which knits them together, each into the other, as it processes its relation to its context, or world. For ultimately, what a mind does is produce a world from a series of realities, just as matter shatters worlds back into semi-compossible realities, only to be recomposed by intertwined networks of minds at further stages in this cycle. In this sense, worlds and realities are differing aspects of the same. Both worlds and realities, however, are always exceeded by the world of which they represent graspings.

THE WORLD. All entities in a given universe ultimately share the same basic reality, known as the world. The world is a reality and world as well as universe, for it is both between and beyond these very categories. As the universe, the world is no different therefrom, for the universe is the manner in which it experiences itself, and hence, there is a difference in name and emphasis only. As a world, the world is the manner in which the universe experiences itself. As a reality, the world is extremely fuzzy, due to the extreme degree of difference between the realities of which it is composed.

MAPPING. Realities and their aspects appear to minds, if in a different manner than worlds and their aspects. Non-conscious minds are affected by their worlds, by they do not know them. Likewise, they are affected by the realities within which they exist and which they give rise to, for entities may grasp their worlds in manners which have symmetry between them, and lead to symmetries in the realities which form between them. Only conscious minds, however, posess the ability to recognize distinct entities, and by means interactions with entities repeated over spacetime, construct maps of the symmetries at work within the reality shared by entities in a particular zone of the world and the conscious mind in question. Doing this intentionally by means of a series of controlled interactions with these entities is known as reality testing, or experiment. Mapping is one key way in which conscious minds work to increase their sync with their worlds.

QUANDARY. All attempts to know matrix have limits. These derive from both the open, intertwined, and extended manner in which emergence manifests itself within the world, but also from the inherent difference between knowledge and understanding. When an attempt is made to capture aspects of the world within knowledge, its conceptual and representational form mesh better with some aspects of the world, but less with others. This is because aspects of the world may be relatively static, situated, and isolated for periods of time, even if they are ultimately necessarily relational in nature. When an attempt is made to fix these relatively reified aspects of the world in knowledge, entities which use these forms of knowledge to organize their relation to the world may do so without experiencing large difficulties coordinating their relation to the world, or within the systems of knowledge they produce. But as knowledge approaches more liminal, processural, emergent, extended, or otherwise unreifiable aspects of the world, the result is paradox, quandary, and infinite regress. This limit to knowledge is what is known as the fundamental obstacle. There are three sides to this obstacle. From an epistemological-diagrammatological perspective, the fundamental obstacle and its varied aspects are the result of what is known as the network paradox. Networks foreground aspects of the world, such that what is left out forms the network’s ground. Any attempt to know the ground in question results in the formation of a new network, but the same problem is ultimately reproduced within this new network formation. Even when an attempt is made to know the world via a series of nested and interlinked dynamic networks, there will always be that which grounds this complex meta- network, and which therefore connects it to the open. In this sense, the structure of inside, boundary, outside is found, if differently, in each of the fundamental obstacle’s manifestations, and these correspond in their way to node, link, and ground, respectively, with each node itself being composed of networks nested within it in turn. The infinite regresses which occur within paradox and quandary are a function of the manner in which the network paradox plays itself out in a wide variety of forms. From an ontological perspective, the fundamental obstacle appears as the quandary of emergence. Emergence is the name given to the self-containing aspects of the world. Since all the world is emergent, if in differing degrees of intensity and in different forms, this means that different aspects of the world will evidence the paradoxical nature of networks in differing degrees and in different forms. The intersection of the network paradox and the quandary of emergence give rise to the fundamental obstacle in its many appearances. However, there is also an ethical aspect to the fundamental obstacle as well, namely, the appeal of the other. Since emergence is fundamentally unknowable, giving rise to paradox within systems of knowledge in its wake, this means that all systems of knowledge must be seen as provisional tools to increase understanding, rather than ends in themselves. The world as emergent is continually in relational and in-process. This means that its otherness from what we know is continually appearing. Only when we continually listen to this appeal can we use knowledge in a manner which is less reifying, more relational, and hence, less paranoid in structure.

OBSTACLE. When attempts are made to know aspects of the world in ways which violate the network paradox, the result is one three types of error, namely, those of experience, distinction, and completion. When these errors arise, we say that the knowing system has fallen into the representational trap, and we can tell this has occurred because the actions of the knowing system in question which are based upon these errors will often fail to sync with the world in which they find themselves. Each of the three types of error lines up with one aspect of the network paradox, such that errors of experience are forms of overnoding, errors of distinction are forms of overlinking, and errors of completion are forms of overgrounding. When a knowing system acts as if a network it uses to know the world matches exactly the contents of a network in the world beyond it, we say that this is an error of experience. This manner of error is an attempt to reduce the oneand to the one(and). This error occurs due to three fundamental manifestations of the fundamental obstacle, namely, the obstacles of matter, privacy, and the context. That is, a knowing subject can never know whether or not its representation of the experience of a matter, other mind, or the context of any entity is the same as its representation thereof. When a knowing system acts as if the distinctions given rise to by means of the networks it uses to know the world matches exactly those in the world beyond it, we say that this is an error of disctinction. This manner of error is an attempt to reduce the twoand to the two(and). This error occurs due to three fundamental manifestations of the fundamental obstacle, namely, the obstacles of decision, experience, and complexity. That is, a knowing subject can never know whether or not the distinctions it makes by employing representational networks to know the world are the same as those in the world itself. Thus, when a subject attempts to distinguish between the contribution of its own networks and the world in regard to a given experience, the subject cannot know the degree to which this distinction is itself the result of the networks it employs or the experience in question. This is known as the obstacle of experience. Likewise, when a subject attempts to distinguish between it’s own contribution and those of one of its subminds when that mind makes a decision, the subject cannot know the degree to which the distinction is itself the result of the networks it employs, or of its submatters. This is known as the obstacle of decision. And in complex systems in the world, whenever a subject attempts to know the degree to which the complexity of a system as a whole is due to the contribution of the submatters in question, the system as a whole, or the potentials relevant to the system in question, the subject cannot know the degree to which the networks formed by means of the perspective taken by the subject in question informs such a judgement. This is known as the obstacle of complexity. And when a knowing subject acts as if it is able to know by means of its representational networks all that is about a given entity, we say that this is an error of completion. Errors of completion are attempts to reduce the threeand of the ground to the three(and). Thus, when a subject acts as if its representations of a system are complete, without taking into account the manner in which all matrix can differ from itself, depending upon the context, we say that there is a manifestation of the obstacle of potential. When a subject acts as if it can know all that is about the world as a whole, thereby reifying the world from process, we say that there is a manifestation of the obstacle of the world. And when a subject acts as if it can know all that there is about a system, thereby denying the relational nature of all that is, we say that there is a manifestation of the obstacle of aspect. Beyond all of these forms of obstacle, whenever any of the errors in question are made in a manner that applys to levels, we say that there is an error of leveling, and that there is a manifestation of the obstacle of level. The obstacle of level may manifest in all the other forms of error and obstacle, for it describes a form of overleveling, an attempt to reduce the threeand to the three(and) of the level. Often these errors intertwine, layer, and interpenetrate, and there are wide varieties of intermediary formations. The reasons for the obstacles described here will be developed in later sections. However, it must not be thought that these obstacles occur due to magical or transcendent reasons. Rather, they spring from the basic relational form of what is. It must also not be thought that these obstacles are merely hindrances. Rather, they describe the manner in which the world remains open. That is, each obstacle is also an opening, and describes the manner in which relational wholes are not closed to change and the new. The ramifications of these issues will be described in full in sections later in this work.