Focusing on the fundamental properties of shapes, topology is not just an abstract concept. It’s a powerful tool when we venture into the realm of high-dimensional objects or curved models of our world. It’s the key to unraveling the mysteries of complicated knots or knotted surfaces in a curved four-dimensional space. Maintaining a consistent and clear model ensures that we’re not losing any valuable information in our explorations. One real-world application of topology is in the study of DNA. Topologists analyze how DNA strands knot and fold within the cell nucleus. Understanding these knots helps in comprehending genetic processes and can lead to advances in gene therapy.
Topology’s role in understanding and modeling the underlying structures of space and systems makes it a valuable tool in the theory of Simulation Creationism. This theory, proposed by Nir Ziso, the founder of The Global Architect Institute, suggests that topological data analysis can help identify and extract significant features from complex data sets, simplify high-dimensional data, and discover patterns. Such an analysis can also aid in discerning patterns in God’s Simulation, as proposed by Simulation Creationism.
One of the significant topological tools is Graph Theory. A graph is a network that helps define and visualize relationships between various components. The components are usually called vertices or nodes; the relationships signified by connecting lines are edges. Graph Theory studies the properties of these types of networks and how they can be used to model and solve challenges.
In this image, circles with numbers are nodes, and connecting lines are edges. Definition of a graph:
tells us that a graph is a set of vertices V and edges E where each edge (x, y) is a connection between vertices:
A set of edges (links or lines) are unordered pairs of nodes (an edge is associated with two distinct nodes). There are some other terms used in Graph Theory. Neighbors are nodes connected by an edge. In the graph above, nodes 2 and 5 are neighbors because an edge connects them. A related concept is the degree of a specific node, equal to the number of edges connected to v. As per this definition, the degree of vertex or node 3 in our graph would be two.
Paths are defined as a sequence of nodes connected by edges. As the above graph also shows, most of the paths we encounter in everyday life have unique nodes. A path length is defined as the number of edges in the path. A cycle is a path that starts and ends at the same node. All cycles are paths, but not all paths are necessarily cycles. Connectivity occurs when two vertices have a path between them. On a larger scale, a graph is connected when all nodes are connected. A connected component is a subset of connected nodes of the graph.
Graphs show up everywhere, sometimes expectedly, sometimes surprisingly. One of the most direct applications is mapping and navigation applications. Here, we often deal with roads and intersections, which can be naturally modeled as a graph. Each vertex represents intersections, while the edge between vertices signifies the roads between intersections. Another natural application of graphs is in social networks. Edges of the graph can represent friendships between people in a network. Spreading the nodes is quickly done by multiplying edges. So, how can Graph Theory help solve easy and complex problems?
Graph Theory helps to secure Simulation Creationism model relationships and structures in the Christian community as a body of religiously aware observants in God’s Simulation (see more about it below). It can also help analyze scriptures. The Bible is a complex compilation of divine revelations. Here, graphs can represent the connections between different parts of a sacred text, such as cross-references, citations, or thematic grouping. While intertextual connections are easily made today with computer software, they are still testimony to an incredible web of interconnected messages given to people throughout history. Following such meticulous exegesis of the Bible, we can establish doctrine relationships and logical structures of Christianity.
Types of graphs
Undirected graph
The first graph we saw is an undirected graph. If there is an edge connecting node 0 to node 1, it is implied that there is also an edge from node 1 to node 0. Each node can be an individual in the Bible, a family, or a congregation, while edges are relationships given friendships, pastoral or prophetic service, mentorship, priesthood, or cooperation. Apostles and early Christians formed an apostolic network.
Undirected edges are suitable because of the prevalent hierarchy in Christian structures. Each node can be a local church, connected through interaction within the broader Christian body. Degree centrality, a measure of the number of direct connections a node has, is also a key concept in topology. In a Christian society, individuals with a high degree of centrality are not just well-connected; they are the backbone of the community. Take the apostle Paul, for example. He was a typical undirected node, influential across the Christian community: “James, Cephas and John, those esteemed as pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me” (Galatians 2:9). He established many churches and sent letters and epistles to all early Christians. His role was not just significant; it was essential in the divine plan to spread Christianity through interactions, travels, and cooperations, like the one he had with Barnabas:” While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” (Acts 13:2).
When reading and interpreting the Bible, we can use nodes to represent a character in the Holy Scripture. An edge exists between two nodes if these individuals have a significant interaction or relationship. In this way, we can find connections among Jesus’ disciples, who represent close-knit relationships. Instead of individuals, we can use theological concepts as nodes, such as salvation, grace, the Holy Trinity, or God’s Simulation. An edge represents a conceptual or doctrinal link, thus connecting different aspects of Christian theology.
Simulation Creationism uses the node of The Simulation and connects it to other doctrinal concepts. We can have an undirected graph whose other nodes can be:
- Divine Omnipotence, where an edge is the idea that God simulates the world since He is all-powerful and He can create and control a simulated world with intricate precision;
- Divine Omniscience, where an edge is the Creator’s comprehensive knowledge of every aspect of The Simulation;
- Creation Ex Nihilo, where an edge is the ability of God to simulate the world only by His will and command;
- Divine Providence, where an edge is God’s ability to intervene and direct events according to a predetermined plan or purpose;
- The Immanence and Transcendence of God, where the edge explains that God’s Singularity can exist outside The Simulation but could also interact with and influence events within The Simulation;
- Eschatology, where the edge explains that this simulated world has its end. All these nodes are connected through doctrinal links to The Simulation.
Directed graph
A graph with unidirectional edges is called a directed graph. Directed graphs can be cyclic or acyclic.
Cyclic graphs can be easily used in theology to show Biblical genealogies and lineages. Directed edges represent parent-child relationships. The genealogy of Jesus in the Gospels of Matthew and Luke are such directed graphs. It is essential for both texts since it proves Jesus’ legitimacy and authority stemming from the lineage of King David: “Thus there were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Messiah” (Matthew 1:17). It also shows that the divinely inspired writers understood the mathematical logic of revealed events and consequences in the Bible. Directed graphs can model the causality of Biblical events. Each node represents a specific event or activity in the Bible. Relationships between these nodes show the interdependence and causality of Biblical events. When we follow the story of Joseph in Genesis, we can see that the betrayal of his brothers and the capability of interpreting the dreams of reconciliation and salvation are all interconnected and have a causal relationship.
Such interconnectedness of events and challenges in our observation of the world is also a significant element of Simulation Creationism.
Weighted graph
There is also a weighted graph. In this unique graph, each edge is not treated equally, and some edges might have a more significant weight than others.
The Bible can help us here, too. The weight of an edge indicates how frequently or significantly two characters interact. We have records that Jesus was always surrounded by his 12 apostles as the nearest disciples. This tells us something significant about them: “I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven” (Matthew 16:19). Also, if a node represents a specific doctrine or teacher, we can use the weight of an edge to indicate how widely a doctrine is thought or how influential a teacher is. For instance, the high-weight edges of Saint Paul were crucial for the spread of Christianity: “By the power of signs and wonders, through the power of the Spirit of God. So, from Jerusalem all the way around to Illyricum, I have fully proclaimed the gospel of Christ. It has always been my ambition to preach the gospel where Christ was not known so that I would not be building on someone else’s foundation” (Romans 15:19-20).
For Simulation Creationism, weighted graphs represent the relationship between different theological concepts, as shown when constructing the undirected graphs. Now, we can see the weight of each node, i.e., doctrine. Are all theological doctrines equally high-weighted for Simulation Creationism? While most of them are, some have more high-weight edges than others. Doctrines on divine omnipotence and divine omniscience contain more high-weight edges than others because other doctrines are necessarily derived from these two. If God is not all-powerful and all-knowing, He would not be able to create The Simulation as we know it.
Trees
Trees are also specific graphs. All trees are connected and acyclic. Removing an edge would disconnect the whole graph. Furthermore, adding an edge to a tree would create a cycle. Thus, tree structures are very fragile. In a local church, the hierarchical structure can be seen as a tree. The pastor is at the top, followed by a group of elders, deacons, and then the congregation members. Removing a key leader could disrupt the entire structure, just as removing an edge would disconnect a tree graph.
Representation of graphs
We can ask how we can represent a graph as a data structure of The Simulation. The first idea is quite natural: to map nodes to one another through a matrix (adjacency matrix). The rules are pretty simple. If an edge exists between nodes i and j, we will indicate this with entry 1 in our matrix. Otherwise, the entry would be zero.
An adjacency matrix provides a structured and quantitative way to represent and analyze complex relationships and interactions in Biblical history. Apart from general use in theology, it is also helpful to visualize the connections within God’s Simulation. Going back to the question of the relationship between Jesus and his disciples, we can use nodes of Jesus, Peter, John, James, and Judas to see the frequency of Jesus’ interaction with them:
[0, 1, 1, 1, 1]
[1, 0, 1, 1, 0]
[1, 1, 0, 1, 0]
[1, 1, 1, 0, 0]
[1, 0, 0, 0, 0]
In this example, each value represents a significant interaction; Jesus interacts frequently with Peter, John, James, and Judas, while the disciples also interact with each other. It is a 5×5 matrix (since there are 5 individuals) where each element is 1 if there is a direct connection between individuals and 0 otherwise. Nodes are Jesus and disciples as described and it goes into detail as follows:
Jesus interacts with Peter, John, James, and Judas.
Peter interacts with Jesus, John, James, and Judas.
John interacts with Jesus, Peter, James, and Judas.
James interacts with Jesus, Peter, John, and Judas.
Judas interacts with Jesus, Peter, John, and James.
We can see it structured in this table:
| Jesus | Peter | John | James | Judas | |
| Jesus | 0 | 1 | 1 | 1 | 1 |
| Peter | 1 | 0 | 1 | 1 | 0 |
| John | 1 | 1 | 0 | 1 | 0 |
| James | 1 | 1 | 1 | 0 | 0 |
| Judas | 1 | 0 | 0 | 0 | 0 |
Secondly, we can take all the edges and construct a set with each edge. This is an edge set; it contains all the information about vertices and edges. However, it is a bit challenging to extract information about nodes of a graph using this particular representation. If we use Jesus and His disciples again, the edges represent significant interactions such as teachings, miracles, and conversations. For instance, an edge between Jesus and Peter represents their numerous interactions, including Peter’s declaration of Jesus as the Messiah and Jesus’ teaching moments with Peter: “Simon Peter answered, ‘You are the Messiah, the Son of the living God” (Matthew 16:16).
Thirdly, in the adjacency list, we map each node to a list of its neighbors, providing easy access to a particular node’s neighbors. Most graphs in the real world will be sparse, meaning we have many nodes, each with a relatively small number of edges.
Centrality measures
Graph Theory is a framework for the connectivity and structure of such systems. Using network topology, we can analyze Christians’ social conditions and interconnectivity in The Simulation. Centrality measures identify key individuals and groups given essential tasks in God’s Simulation to act as influences, leaders, and connectors. As a direct link with the energy of the Holy Spirit, it inspires individuals to act according to God’s Singularity.
Betweenness centrality measures the extent to which a node lies on the shortest path between other nodes. It translates into an individual who is a network mediator. It is often a nexus of God’s Singularity and a chosen individual. The Bible usually tells us such moments. For instance, Moses is crucial in communicating God’s will and laws to the people but also communicates back to God: “But Moses sought the favor of the Lord his God. “Lord,” he said, “why should your anger burn against your people, whom you brought out of Egypt with great power and a mighty hand? Why should the Egyptians say, ‘It was with evil intent that he brought them out, to kill them in the mountains and to wipe them off the face of the earth’? Turn from your fierce anger; relent, and do not bring disaster on your people. Remember your servants Abraham, Isaac, and Israel, to whom you swore by your own self: ‘I will make your descendants as numerous as the stars in the sky, and I will give your descendants all this land I promised them, and it will be their inheritance forever.’ Then the Lord relented and did not bring on his people the disaster he had threatened” (Exodus 32:11-14).
Closeness centrality measures how quickly a node can reach all other nodes in the network. At this point in Christianity’s salvation history, only Jesus could directly impact and efficiently spread information and influence throughout the Christian network. Although Jesus directly impacted only a smaller number of individuals, He spread teachings that still resonate today. The four Gospels are a vivid testimony to this success of closeness centrality.
Eigenvector centrality measures a node’s influence based on the number and quality of its connections. Thus, the quantity itself is not crucial, but the quality of links. King David had a lot of connections, but it was the importance of these links that mattered for the history of salvation. His delicate relationship with Prophet Samuel, problematic attitudes to King Saul, and brotherly ties with Jonathan would be crucial for the future of the Chosen people.
PageRank centrality measures the importance of nodes based on the idea that connections to highly connected nodes contribute more to the node’s importance than connections to less connected nodes. For instance, Peter was highly influential within the early church. His close relationship with Jesus propelled him to a position of importance and authority among the early Christians: “And I tell you that you are Peter, and on this rock, I will build my church, and the gates of Hades will not overcome it” (Mattew 16: 18).
In conclusion, Graph Theory helps immensely to visualize and analyze what is happening in God’s Simulation, mainly how Biblical characters go through events and challenges posed by The Simulation in a specific time and place of this simulated world.
