Discrete Physical Models - Revision history

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‎The Wolfram Physics Project (Hypergraph Language)

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‎The Wolfram Physics Project (Hypergraph Language)

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‎The Wolfram Physics Project (Hypergraph Language)

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 * There are several well‑established terms, each emphasizing a slightly different reason why calculus breaks down.
 * The formal concept of string rewriting was first introduced by the Norwegian mathematician Axel Thue in 1914. He wanted to see if he could transform one string of symbols into another using a fixed set of rules He proved that determining if one string can be transformed into another is often "undecidable."
-* A few years later Max Born decided that continuous Schrodinger Equations could be used to set the environment where a Heisenberg "event" could occur. Von Neumann and Dirac set the focus on continuous functions that still dominate physics.
+* A few years later Max Born decided that continuous Schrodinger Equations could be used to set the environment where a Heisenberg "event" could occur. Von Neumann and Dirac set the focus on continuous functions that still dominate physics. See the following wiki where the [[Eventful Universe]] is explored in more detail.
 * Emil Post, an American logician, independently expanded on Thue's work in the 1930's. He created "Post Production Systems. Post viewed mathematics itself as a series of string-rewriting steps. He famously showed that his simple systems were "Turing Complete" (meaning they could compute anything a computer can compute). Post’s work suggested that the universe doesn't need "numbers"; it only needs symbols and rules to function.
 * Noam Chomsky's original formulation of generative grammar in the 1950s was explicitly defined as a system of rewriting rules which are seen in some of the following solutions.

@@ Line 9: / Line 9: @@
 * There are several well‑established terms, each emphasizing a slightly different reason why calculus breaks down.
 * The formal concept of string rewriting was first introduced by the Norwegian mathematician Axel Thue in 1914. He wanted to see if he could transform one string of symbols into another using a fixed set of rules He proved that determining if one string can be transformed into another is often "undecidable."
-* A few years later Max Born decided that continuous Schrodinger Equations could be used to set the environment where a Heisenberg "event" could occur. Von Neumann and Dirac set the focus on continuous function that still dominate physics.
+* A few years later Max Born decided that continuous Schrodinger Equations could be used to set the environment where a Heisenberg "event" could occur. Von Neumann and Dirac set the focus on continuous functions that still dominate physics.
 * Emil Post, an American logician, independently expanded on Thue's work in the 1930's. He created "Post Production Systems. Post viewed mathematics itself as a series of string-rewriting steps. He famously showed that his simple systems were "Turing Complete" (meaning they could compute anything a computer can compute). Post’s work suggested that the universe doesn't need "numbers"; it only needs symbols and rules to function.
 * Noam Chomsky's original formulation of generative grammar in the 1950s was explicitly defined as a system of rewriting rules which are seen in some of the following solutions.

@@ Line 9: / Line 9: @@
 * There are several well‑established terms, each emphasizing a slightly different reason why calculus breaks down.
 * The formal concept of string rewriting was first introduced by the Norwegian mathematician Axel Thue in 1914. He wanted to see if he could transform one string of symbols into another using a fixed set of rules He proved that determining if one string can be transformed into another is often "undecidable."
-* A few years later Max Born decided that continuous functions could be used to set the environment where a Heisenberg "event" could occur.
+* A few years later Max Born decided that continuous Schrodinger Equations could be used to set the environment where a Heisenberg "event" could occur. Von Neumann and Dirac set the focus on continuous function that still dominate physics.
 * Emil Post, an American logician, independently expanded on Thue's work in the 1930's. He created "Post Production Systems. Post viewed mathematics itself as a series of string-rewriting steps. He famously showed that his simple systems were "Turing Complete" (meaning they could compute anything a computer can compute). Post’s work suggested that the universe doesn't need "numbers"; it only needs symbols and rules to function.
 * Noam Chomsky's original formulation of generative grammar in the 1950s was explicitly defined as a system of rewriting rules which are seen in some of the following solutions.

@@ Line 9: / Line 9: @@
 * There are several well‑established terms, each emphasizing a slightly different reason why calculus breaks down.
 * The formal concept of string rewriting was first introduced by the Norwegian mathematician Axel Thue in 1914. He wanted to see if he could transform one string of symbols into another using a fixed set of rules He proved that determining if one string can be transformed into another is often "undecidable."
 * Emil Post, an American logician, independently expanded on Thue's work in the 1930's. He created "Post Production Systems. Post viewed mathematics itself as a series of string-rewriting steps. He famously showed that his simple systems were "Turing Complete" (meaning they could compute anything a computer can compute). Post’s work suggested that the universe doesn't need "numbers"; it only needs symbols and rules to function.
 * Noam Chomsky's original formulation of generative grammar in the 1950s was explicitly defined as a system of rewriting rules which are seen in some of the following solutions.

@@ Line 9: / Line 9: @@
 * There are several well‑established terms, each emphasizing a slightly different reason why calculus breaks down.
 * The formal concept of string rewriting was first introduced by the Norwegian mathematician Axel Thue in 1914. He wanted to see if he could transform one string of symbols into another using a fixed set of rules He proved that determining if one string can be transformed into another is often "undecidable."
 * Noam Chomsky's original formulation of generative grammar in the 1950s was explicitly defined as a system of rewriting rules which are seen in some of the following solutions.

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 * Exploring where “the realm where continuity and differentiability stop being good models,”.
 * There are several well‑established terms, each emphasizing a slightly different reason why calculus breaks down.
 ===Breakdown of the continuum approximation===

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 In the Wolfram Model, General Relativity isn't "programmed in" via equations; it emerges as a statistical consequence of millions of discrete updates, much like how the smooth behavior of a fluid emerges from the chaotic bouncing of individual molecules.
 The bridge between discrete rewriting rules and Einstein’s equations relies on three main pillars:
-####The Emergence of Manifolds (Space)####
+====The Emergence of Manifolds (Space)====
 In traditional physics, space is a continuous "background" (
 ). In this model, space is a discrete hypergraph.
@@ Line 313: / Line 313: @@
 Gravity	Curvature of the manifold	Local variation in the graph's structure
 The Mathematical Link: As of 2026, researchers have shown that for any rule that is Causally Invariant (meaning the order of updates doesn't change the outcome), the large-scale limit of the causal graph must satisfy Einstein’s Field Equations. Essentially, if the graph is consistent and large enough, it is forced by logic to behave like gravity.
-####Why this matters for 2026 Research####
+====Why this matters for 2026 Research====
 By treating gravity as a discrete rewriting process, physicists are now using these rules to model Singularities (like the centers of black holes). In continuous calculus, equations "break" at a singularity (division by zero). In a discrete model, the graph simply becomes extremely dense or stops updating, allowing researchers to simulate what actually happens to "information" inside a black hole without the math crashing.

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 In the Wolfram Model, the "rewriting rules" are the fundamental "engine" of reality, replacing continuous differential equations with discrete, local transformations of a spatial hypergraph. As of 2026, these rules are understood as the mechanism that "knits together" the structure of space and time.
-####The Anatomy of a Rewriting Rule####
+====The Anatomy of a Rewriting Rule====
 A rule consists of a template (input) and a replacement (output).
@@ Line 241: / Line 241: @@
 YouTube
-####Time as Computational Step####
+====Time as Computational Step====
 Unlike traditional physics where time (
 ) is a continuous parameter, time in this language is the actual act of applying a rule.
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 Computational Irreducibility: You cannot "calculate" the future state of the universe without actually running the rules; there is no mathematical shortcut (like a closed-form equation) to skip steps.
-####Multiway Systems & Quantum Physics####
+====Multiway Systems & Quantum Physics====
 When multiple rules can be applied to the same part of a graph, or a rule can be applied in multiple locations, the system branches. This is called a Multiway System.
 The Wolfram Physics Project
@@ Line 257: / Line 257: @@
 Wolfram Institute
-####Ruliological Engineering####
+====Ruliological Engineering====
 Recent work in 2026 (referred to as "ruliological engineering") focuses on identifying which specific rules generate familiar physical geometries:
 Wolfram Community
@@ Line 296: / Line 296: @@
 , the rule is creating 2D space; if
 , it's 3D.
-####The Causal Graph (Space-Time)####
+====The Causal Graph (Space-Time)====
 This is the most critical conceptual leap. While the hypergraph represents space, the Causal Graph represents spacetime.
 Events as Nodes: Every time a rewriting rule is applied, it is considered an "event."
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 Light Cones: This graph of dependencies naturally forms "cones" of influence. Information cannot travel through the graph faster than the rule-application rate, which effectively sets the speed of light (
 ).
-####Curvature as Graph Density####
+====Curvature as Graph Density====
 In General Relativity, gravity is the curvature of spacetime (
 ). In the Wolfram Model, curvature is a measure of graph thickness and connectivity.
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 By treating gravity as a discrete rewriting process, physicists are now using these rules to model Singularities (like the centers of black holes). In continuous calculus, equations "break" at a singularity (division by zero). In a discrete model, the graph simply becomes extremely dense or stops updating, allowing researchers to simulate what actually happens to "information" inside a black hole without the math crashing.
+====explore how Energy and Mass are defined in this system====
 In the Wolfram Model, because there is no "matter" and "space" (only the hypergraph), energy and mass must be properties of the network’s connectivity and its evolution over time.
 Essentially, energy is the rate of activity, and mass is the "resistance" or persistence of that activity.
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 This discrete approach suggests that the vacuum itself is "hot" with activity. Would you like to explore how the Vacuum is modeled as a sea of constant rewriting, or should we look at how this leads to Quantum Uncertainty?
 How does this lead to quantum uncertainty?