Genesis Ex Nihilo

Genesis Ex Nihilo In Principio Erat Creatio Christopher J. Cole April 14, 2025 Chapter 1 Fundamenta 1.1 Creator, Creation, Creativity Creation begets creation, therefore creation is also creator. To be creative requires creation, but not all creation is necessarily creative. So then, what is creativity? The most fundamental acts of creativity are functors of order and chaos itself. Objectively, order implies congruence with the governing axioms of a universe. Chaos then, is objectively defined as incongruence with the governing axioms of a universe. A functor is a function whose operands are not always concrete; consider a functor which inputs other functions, or processes. All creations assume the role of creator, but not all creators are creative. 1.2 Axiomatica, Mechanica Let us consider a domain as a formal system defined by two interdependent components: a set of axioms and a collection of mechanics. In this context, axioms are the foundational, incontrovertible propositions that serve as the primary constraints or permissions of the system. They represent fundamental truths which are assumed without proof. Axioms and Their Classes Axioms can be classified into three distinct categories: 1. Permissive Axioms: These axioms assert the existence or instantiation of a property or entity. For example, the axiom “Let there be light” posits a basic state of existence for light within the domain. 2. Restrictive Axioms: In contrast, restrictive axioms impose constraints or negations. An axiom such as “Let there not be light” serves to delimit or even invert the condition established by a permissive axiom. 3. Causative Axioms: These axioms are responsible for instantiating behaviors or dynamic properties within the system. For instance, the causative axiom “All liquids flow uphill” does not merely state a property of liquids; it defines a dynamic behavior that is applied to the entities governed by permissive or restrictive axioms. In essence, while permissive and restrictive axioms define the static properties of a domain (i.e., its skeleton), causative axioms drive the evolution or behavior of these properties by introducing interactions and dependencies. 1 A simplistic example using Cole Notation (explained in depth momentarily) demonstrating the basic interplay bewteen these axioms is as follows: Ap|r Ac(1.1) The loop arrow signifies that the causative mechanism continuously or repeatedly applies to the initial axiom, thereby governing its operational behavior within the domain. Mechanics as Interactions Between Axioms Mechanics are defined as the rules governing the interactions among axioms. They encapsulate how axioms complement or contradict each other within the domain. Formally, mechanics can be viewed as mappings or relations that specify the conditions under which the properties prescribed by individual axioms are activated or inhibited. For example, given: •Axiom: “Let there be trees” (Permissive) •Axiom: “All trees grow to ten meters tall” (Causative/Restrictive) •Axiom: “Let there be fruit” (Permissive) •Axiom: “Let all trees ten meters tall bear fruit” (Causative/Restrictive) The following set of axioms create a mechanic whereby trees must grow to ten meters tall, then produce fruit. This is called a mechanic because a causative axiom dictates the interplay between the trees and thefruit; this alone is enough to define a mechanic, however there is a secondary causative axiom which dictates the interplay between the tree and its own growth. Note that in this example, no axiom instantiates time or other fundamental rules which reality has. Herein lies the power of created domains; anything and everything is possible. Cole Notation for Domain Schematica To represent the interplay between axiom types and the creation of mechanics, the author presents a notation to aid in the comprehension of domains. The previous example of trees and fruit can easily be converted to Cole notation to demonstrate their interplay1: Atree A10m tall Afruit AgAb(1.2) And the formalization of the definition of a mechanic can be easily distilled into the following schematic: Ap|rAp|r Ac(1.3) 1.3 Fundemental Creative Acts 1.3.1 Pure Genesis Functors Xenogenetica is one such fundamental act, precipitating chaos from order. Orthogenetica complements xenogenetica, precipitating order from chaos. Concomita is the fundamental act of precipitating order from order. Abstractica is the compliment of concomita, precipitating chaos from chaos. There four functors are members of the class ”Pure Genesis”, meaning such functors are the highest possible order of creativity. Below this class lies ”Elementary Genesis”. All elementary creative functors derive from pure genesis functors. 1Where Agrepresents the growth axiom and Abrepresents the fruit-bearing axiom. 2 1.3.2 Elementary Genesis Functors There are infinitely many Elementary Functors, however, we may make note of Boden’s functors to establish a baseline: •Transformation •Generation •Combination The author notes that there are additional, a likely infinite amount of such elementary functors; this is because the three primary elementary functors are derived from basic compositions of the pure genesis functors, and there can indeed be many compositions of these functors to encode an infinite number of creative functors. One such functor the author would like to highlight is instantiation. Instantiation is the ability of a sufficently intelligent creation to create its own domain within the universe it resides in. For instance, take a sufficently intelligent creation, C0.C0resides in universe U.C0can instantiate a domain, DC0with its own axioms and mechanics. This action is denoted by: C0DC0 ins (1.4) Every created object C0∈DC0inherits a subset of the axioms governing an instantiated domain, DC0. This also applies to creators within DC0. Now, then the frame of reference becomes of the utmost criticality. From what reference point are creations creative? Boden’s model only accounts for two frames of reference: P-creativity (psychological) and H-creativity (Historical). These frames of reference are simply not enough to fully encompas the true scope of creativity. P-creativity assumes intelligence of a creator, and H-creativity assumes that time is a parameter of the universe where creativity is to be assessed. We need something more powerful. 1.4 Frame of Reference Frame of reference is crucial for creativity, as no entity within a universe can perform pure genesis in that universe– meaning it cannot manipulate the very fabric, or governing axioms of that universe. To illustrate the concept, take for example, a rock (creation) in base reality2. A weathering of this rock from the perspective of a non-entity (another creation in base reality) would be a creative process perpetually, because the product is continually novel. This is because the rock does not know it is a rock. To the creator of weathering and the rock(s), this is a process of concomita, as both weathering and the precipitate of that weathering is ordered, or known to its creator. Let’s do another example in base reality. Assume W = Water, F = Fire. If C1applies a creative functor to W and F, precipitating steam (S). To an observer, C2, who observes this operation and has not seen this specific operation (and precipitate), this is a creative act. If perhaps, C2has seen the specific operation but not the precipitate in the past, and now observes the precipitate, this is a latent creative act. The inverse, however, is not a latent creative act. If C2has previously seen Steam, the operation(s) leading to such discovery is in itself a creative act. All creative acts utilize some number of axioms, and output both a precipitate and an underlying axiom. A created domain may have an axiom ”When heat is applied to liquid, steam is created”. If C1combines Fire and Water, it reveals the axiom (though only to a partial degree), as well as a new malleable axiom (symbol) from C1’s perspective, S. Truly, every elementary creative act calls upon the pure genesis functors to some degree. For every act of elementary genesis in some way derives from the pure genesis functors. For a sufficiently intelligent creator, the ability of instantiating domains is possible. The observer (of C1’s creation of steam) C3has its own created domain. WIthin this domain DC3, it has the ability to use pure genesis (from the perspective of creations within it). That is, it can create, modify, and remove axioms from it. Such domains may be partially shared with other sufficiently intelligent creators, meaning that multiple 2“Base reality” refers to our universe, where we exist 3 creators may exercise pure genesis over that created domain. All creations and axioms and creations within DC3are attributed to C3and any collaborators. If a creation within DC3were to create steam in DC3, this would be creative only to creations in DC3, if and only if C3has discovered and/or observed steam in base reality. If C3has not created or observed steam, then the creation of Steam is creative to both C3and DC3. In order for axioms, creations, or other domains within DC3to exit and manifest in base reality, it requires a conduit of sufficient permission. That is, If the creator can perform pure genesis operators on a created domain, it can move axioms, creations, mechanics, etc. to another domain of its own creation. If it cannot, it can only approximate this manifestation through elementary creative techniques. This means that axioms, creations, mechanics, etc. created in DC3can only be creative to base reality if base reality is created by C3. Otherwise, it can at most be creative to the creations within base reality or any other created domain within base reality. A creator within its own created domain, may create axioms which do not work in the domain which the creator resides. Axioms created in DC3may not be feasible in base reality, though the host does not know whether or not it works until its tested in base reality. These are called hypothetical axioms. Take for example a created domain (DC), within it, there are marbles: blue marbles, red marbles, and green marbles. An axiom of base realitymight be that Blue marbles combined with Red marbles make purple purple marbles. A creator in base reality C1, attempts to combine a Blue and Green marble, but this does not work. C1 creates a domain, DC1, with an axiom that combining Blue marbles and green marbles makes a red marble. C1then creates three marbles in DC1, a red marble, a green marble, and a blue marble. It then combines them and now there are two red marbles. If an observer, C2, in base reality observing DC1observes this, but not the initial attempt to combine the marbles, C2can be a conduit, and attempt to enact this axiom in base reality I note that from C2’s reference frame, this is a creative act, but from C1’s reference frame, this is merely a repetition of C1’s previous attempt but by C2. From DC’s reference, nothing creative is being produced. From DC1’s reference, the combination of the Blue marble and the green marble was not done before, which revealed a new axiom to C2(but not C1) and gave a creative output from C2and DC1’s frame of reference (but not from C1’s reference because C1instantiated DC1and C1is in base reality so nothing in DC1is creative to base reality. 1.5 Shared Domains, Conduits Shared domains may also be instantiated between entities. Such shared domains rely on a conduit; that is, a mediator between domains. In most instantiated domains, the conduit is the creator of that domain. In shared domains, the properties shift. The most basic method to denote the relationship between a conduit and the creator of a domain is to denote the sharing of both axioms, creations, and nested domains (within the domain) between the domain and its conduit and/or creator. The symbol ℧is used to denote the set of everything within the created domain. One can assert from this a simple definition of ℧:℧={A, M, C, D}. Where A represents the axioms, M represents the mechanics, C represents the creations and creators within a domain, and D represents the subdomains instantiated by any creators in the domain. C0DC0 Ins ℧ ℧′ (1.5) The most basic example to illustrate this concept is to consider the human imagination (which is by nature a created domain). Within one’s imagination, the scenarios enacted within it edify oneself, and, in turn, one may introduce new creations and axioms into the imaginative domain to continue this edification process. In this scenario, the conduit is the owner of the imaginative domain (the human). Conduits of a domain can transfer anything, including the domain itself (if sufficent axioms and permissions exist) to another domain instantiated by the conduit. Consider a creator C0, and two instantiated domains by C0,DC0and DC1, and finally some variable ωsuch that ω∈℧DC0. For ωto go from DC0 4 to DC1, it requires a conduit. In this case, it’s C0because any creator of a domain is concomitantly a conduit. Since C0didn’t instantiate base reality, it is unable to spontaneously precipitate anything from its instantiated domains in base reality. That is, in the example of the imaginative domain, one cannot simply bring something in their imagination into base reality. This is because man is creation within base reality. To illustrate this concept in formal notation, we can say: DC0DC1 ω(1.6) Shared domains in base reality are never truly “shared”. Rather, in base reality, a sufficently intelligent entity provides instructions to instantiate a domain of similar properties. For instance, instructing someone to imagine a reality where “apples are liquid at room temperature” instantiates a domain for any sufficently intelligent entity, however, this domain will vary from person to person. Despite this limitation, high-fidelity domain sharing is an axiomatic decision, and a domain can be instantiated where domains are shared without loss of fidelity. In Cole’s notation, we can denote the relationship between creators and their shared domains. C1 C0SDCC1 C0 ℧ Ins ℧′ conduit Ins (1.7) 1.6 Components of a Domain, Instantia From the rudimentary assertion ℧={A, M, C, D}, we can formally define the components of a domain. To instantiate a domain, the creator must have access to a medium (or media). A medium is defined as a channel through which ℧can flow. This can be the neural makeup of a human, the memory of a computer; it is anything which supports the flow of ℧. Once the chosen media or medium is chosen, the creator can now inject ℧into the domain. The domain lacking ℧is a stagnant domain; meaning, it’s as if it doesn’t exist at all. As soon as ℧is injected into the domain, the domain has substance and is live. Not going forward in exchange of ℧and ℧′begins. The creator puts axioms, mechanics, creations and/or domains within the domain and receives new forms of each as well as new precipitates from that domain. These new forms and precipitates are what comprise ℧′. Consider the following schematic: CℵDCℵ ins ℧ ℧′ (1.8) In the schematic, the injection of ℧into DCℵto instantiate it is an act of instantia. Instantia is the tier of creativity shared by both pure genesis users and sufficently intelligent elementary genesis users. For instance, in base reality, the axiomechanica do not permit a rock to use instantia-tier functors, but humans are. It is also noted that from the frame of reference within DCℵand any entities within it, the injection of ℧is an act of pure genesis. The retrieval of ℧′={A′, M′, C′, D′}from DCℵis an act also of instantia. I conjecture that this enactment of instantia and the exchange of ℧and ℧′represents a fundamental definition of elementary genesis. So, then, it can be conjectured that all elementary genesis functors are an exchange of ℧and ℧′. 1.7 Universa Mechanica Both conduits and instantiatiors can receive ℧′. Depending on axiomatic permissions, a conduit may or may not be able to inject ℧. The instantiatior can always do this, however. Conduits and instantiatiors alike 5 may position themselves within a domain; either creating an entity to manifest in, or inhabiting a creation within the domain— simply receiving ℧′through the creation, hijacking it entirely, or specifying in between. This means that instantiatiors and conduits, while simultaneously existing in base reality (or some external domain outside of the instantiated domain), can exist within other instantiated domains. 1.8 Vantage Vectors, Domain Properties, Planes Instantiatiors and conduits of such potency demand a granular method to evaluate the how information is ingested. This requires a sort of “reverse frame of reference”, meaning that the creator (instantiatior and/or conduit) themselves can modulate their input channels so that what comes in is more novel than what may actually be happening. A simple example within the headspace can be imagined if one first imagines a fantasy landscape, then a pair of yellow tinted sunglasses. If the creator puts the glasses on, the world’s appearance changes. One can imagine a partial or full overlap of the glasses. Overlap (or lack thereof) can happen when the vantage vector changes, causing various compositions of creations depending on the axiomechanics of the domain. However, that is a rather trivial process. This functionality can be extended to entire domains, causing compositions (or lackthereof) of axiomechanica. The precipitate of vantage vectors at the domain level can lead to radical insights and radical new building blocks for new domains. This notion of domain composition implies that sufficiently intelligent creators can manipulate the coordinates determining a domains existence/location across media (or a single medium) which the creator has permission to manipulate. A creator lacking such permission can simply instantiate a plane which does have access to manipulate those “invariable” parameters and copy the domains it wishes to sandbox through ℧. From this, we can extrapolate some properties of domains, and define a couple new ones. The first pair of properties static and dynamic. Static domains do not have a time parameter or any other parameter which permits evolution. Static domains are frozen. Dynamic domains are the opposite, they are liquid. There is both a parameter (not necessarily time) which permits the axiomechanica to evolve, and there is a mechanic evolving ℧in the domain. The second pair of properties is opacity and translucence. Opacity governs how visible a domain is. Low opacity makes a domain less apparent and high opacity makes it very visible. Translucence governs how easily a creator can see inside the domain. Low translucence makes it difficult to peer inside while high translucence makes it very easy to peer inside. These domains reside on a plane. Planes are domains in every sense but a different term is used for clarity. When domains are in a plane, a sufficiently intelligent creator or conduit can now arrange the domains parametrically (if the domains on the plane all have space and time parameters, domains can be arranged spatiotemporally), and manipulate the aforementioned properties. Vantage vectors can be taken according to the instantiator or conduit’s vantage within the plane. This means if the entity gives a partial overlap of translucent, opaque domains, the entity receives ℧′′ =℧′ DC0◦℧′ DC1— a composition of two domains’ ℧′, yielding cross-domain axiomechanica. 1.9 Frame of Reference Revisited What then is creativity? It is any frame of reference which views an axiomechanical interaction and/or precipitate as an act of perceived pure genesis. More formally, it is the observation and/or enactment of ℧ exchange(s) both internally or externally which, from a frame of reference, is seen as perceived pure genesis. Frames of reference have four different types: solid, fluid, latent, and diffusion. Solid frames are static, they are snapshots of a dynamic process or experience and contain only one “viewer”. Solid frames in some sense can be imagined as a photograph. There is one person holding the camera, thus there is only one “viewer”. Fluid frames are a continous set of solid frames which capture the dynamism of a process or experience and also contains only one “viewer”. In similar fashion, fluid frames can be likened to videos. Diffusion frames are collections of static frames which are not necessarily linked (be it by perspective, time, or other paramters) to one another. Diffusion frames evaluate these collections as one single fluid frame. Latent frames, similarly do the same with a collection of not necessarily linked fluid frames. Latent frames evaluate collections of fluid frames as one single fluid frame. Syncopated frames are hybrids of both solid and fluid frames; it is a collection of both solid and fluid frames, and evaluated as one fluid frame. A simple method to grasp this concept is to view number lines with the sole axis being time (t). 6 Element Process Product Solid Frame Fluid Frame U U U A A U U K O O U K U A(A,X) U K K O O K U U X X K U K C(C,O) K K U X X K K K C C Table 1.1: Contingency Table for Solid and Fluid Frames of Reference. t 012345 Solid Frame t 012345 Fluid Frame t 012345 Latent Frame t 012345 Diffusion Frame t 012345 Syncopated Frame Using this framework, it is easy to characterize Boden’s P-creativity and H-creativity. P-creativity is a solid frame from the perspective of the consciousness — a moment where something emerges as a meaningful whole. Boden’s H-creativity is a diffusion frame — a set of discrete known events across the timeline of history, which includes the new idea being evaluated. I say this with directive: Boden’s P and H creativity are two of many; and are fundamentally incomplete in their scope. Thus, I have provided primitives and a taxonomy for constructing and classifying frames of reference. Solid frames only care about element and product. Fluid frames take into account if the process(es) are known or not, whereas solid frames only capture a single state. Table 1.1 shows these contingencies. Processes of percieved concomita can be relegated to uses of elementary genesis functors. This can only happen with fluid frames. This is because solid frames only capture states. The same is true for its counterpart, the diffusion frame. Latent frames, like fluid frames, can discern process. Syncopated frames of fluid frames and solid frames can be used to construct hypotheses or other hypotheticals (i.e. Heat and water make steam (fluid frame) and red water (solid frame)) that can be tested in the entity’s base reality or if sufficent permissions, in a domain. Diffusion frames can be used to make inferences about processes, latent frames can be used to make inferences about the paramaters of a process. Vantage vectors are a component of instantia-tier entities. The vantage vector determines percieved pure genesis with result to an instantiated domain or composite domain. The auxiliary function of the vantage vector is targeted injection of external ℧and targeted exchange of internal ℧. The exchange of ℧can be internal and/or external. External ℧exchange occurs in a domain not instantiated by some entity (i.e. base reality, shared domains, etc.), and internal ℧exchange happens within domains instantiated by some entity. Entities with only external ℧exchange can only store states, whether it be physically, internally, or other. 7