https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Wolfram Fundamental Physics Project with no replies sorted by active. https://community.wolfram.com/groups/-/m/t/3773775 The Ruliad—the entangled limit of all computation—can be constructed with universal computation using nothing but **pure, unlabelled 2D graphs** and a single primitive: the **NAND gate**. ### 1. Empty Vertices as Pure Relations Instead of labeled NAND input and output variables, the vertices are empty identifiers. Values are encoded purely as topological degree (leaf counts): * **Bit 0:** 1 attached leaf * **Bit 1:** 2 attached leaves For example, $1 \text{ NAND } 1 = 0$ is mapped directly to a simple directed graph: ```text Graph[{1->3, 2->3, 3->4, 1->5, 1->6, 2->7, 2->8, 4->9}] ``` * **Inputs (1 & 2):** Each has 2 leaves attached $\to$ **Bit 1** * **Hub (3):** Processes incoming edges to output node (4) * **Output (4):** Has 1 leaf attached $\to$ **Bit 0** ### 2. Timeless Computation & Infinite Unrolling In this framework, execution doesn't happen "over time." Iterative programs and infinite loops are **unrolled spatially** into infinite acyclic subgraphs: * Time becomes graph depth. * A loop isn't a state repeating in time—it is an endless forward path through the net. * The entire execution history exists simultaneously as a static, geometric feature (a Block Universe). ### 3. The Whole Ruliad Because NAND is functionally complete, a network of unlabelled NAND graphs can express any Turing machine or computational state. Unrolling all possible NAND configurations yields the complete Ruliad—achieving full computational universality on the simplest possible topological substrate. Anders Lindman 2026-08-05T12:53:04Z https://community.wolfram.com/groups/-/m/t/3733334 ![Q102 Growth][1] Start with a *bare* hypergraph rewriting system in the spirit of the Wolfram Physics Project: featureless atoms, ternary edges, one local rewrite. Now add a single demand: that the system be **closed to efficient causation** in Robert Rosen's sense, so every producer in the system is itself produced by the system. That one demand is not free. It forces a chain of structure, and what grows out of it is the object in the animation above: a 6-vertex seed that grows, collapses to a 51-class gauge quotient, and doubles under charge conjugation to a 102-vertex object that carries the sign data of a real spectral triple of **KO-dimension 6**. Everything here is exact - Gaussian integers, no floating point, **no random seed** - so the headline count is reproducibly **102**. The full notebook is attached. ## What is Rosen closure? Robert Rosen was a theoretical biologist who asked what *minimally* separates an organism from a machine. His answer: a machine is built and maintained from the outside (its blueprint, its factory, its repairman are all external) whereas a living system is **closed to efficient causation**. "Efficient cause," in Aristotle's sense, is *the thing that brings something about*; closure means every process that produces or maintains a part of the system is itself produced by some part of the system. The system makes its own makers, and nothing in its organization is entailed from outside. Rosen formalized this as an **(M,R) system** (a metabolism together with repair-and-replication maps that the system must generate itself) and the consequence that matters here is that closure forces a **self-referential fixed point**: the system has to be able to produce its own production rules. That self-reference is the entire engine. A Wolfram model's rewrite rule is imposed from outside; demanding closure instead turns the rule into something the decorated hypergraph must reproduce *internally* and that single requirement (next section) is what forces three functional roles, ternary edges, and a continuous ℂ³ colour, with essentially no freedom left. This is *deliberately not* a stock `WolframModel`, and that distinction is the whole point. So, let me start there. ## Why it isn't a stock Wolfram model A `WolframModel` rewrites **bare** hypergraphs: atoms are featureless, and rules are pure connectivity patterns. The moment you impose Rosen closure, the bare atoms are *obstructed* out of every featureless option and **forced** to carry a continuous colour. The forcing chain (each link the unique survivor of an obstruction): - closure needs exactly three functional roles → edges are **ternary** (arity 3); - **no discrete labelling** can satisfy closure → every finite decoration is exhaustively obstructed (all 256 binary rules fail; ℤ₂, ℤ₃, …, ℤ₈ all fail); - the only continuous composition that closes is a **cross product on a 3-vector** (Hurwitz); - and the field must be **ℂ, not ℝ** → the self-referential edge needs an isotropic unit vector (`v·v = 0`), which ℝ³ has none of and ℂ³ does, e.g. `(1, i, 0)/√2`. So the colour isn't an attribute bolted onto a Wolfram model, it's **what closure does to one**. Each vertex carries a colour `ψ ∈ ℂ³`, and the composition rule is forced to be: compose[a_, b_] := Conjugate[Cross[a, b]] (* conj(a × b), exact, unnormalised *) (the conjugation is what keeps it SU(3)-equivariant). The gauge quotient identifies vertices whose colour vectors are linearly dependent over ℂ exactly, with no threshold: rayEquivQ[a_, b_] := AllTrue[Cross[a, b], # == 0 &] (* a ~ b ⇔ a × b = 0 *) Putting a colour on the atoms makes this a *decorated* (attributed) hypergraph rewriting system (close in spirit to **@Ray Aschheim**'s color spin networks, but here the colour, the dimension 3, the cross product, and the conjugation are all *forced*, not posited). ## Exactness matters: 98 vs 102 Because the quotient is by exact ray-equivalence over ℤ[i], the construction is fully deterministic and reproducible. This is not a cosmetic choice: a Float64 fidelity-threshold version of the same construction **merges four genuinely-distinct rays** and reports 98 instead of 102. Exact Gaussian-integer arithmetic gives 102 every time. (For the related question of detecting equivalence on hypergraphs *approximately*, cf. **@Regen Petu-Stiles**'s work on approximate isomorphism. The contrast between exact and thresholded equivalence is exactly where the 98-vs-102 discrepancy lives). Six canonical Gaussian-integer rays seed the system, on the complete ternary topology K₆³ (all 120 ordered triples of distinct vertices): icsBase = {{2+I, 1, 3-I}, {1, 2+I, 1-2 I}, {1-I, 3, 2+I}, {3, 1-I, 1+2 I}, {1+2 I, 2-I, 1}, {2, 1+I, 3}}; ## Growth to Q102 The multiway grows; the colour quotient closes almost immediately. Distinct colour-classes per generation: **6 → 21 → 51 → 51 → 51** — a fixed point at generation 2. ![Distinct Colour-classes vs Generation][2] Side by side: the raw multiway (left, coloured by generation) explodes to 456 vertices, while its exact gauge quotient (right, tier A/B/C) closes at 51. ![Frame 2][3] The charge-conjugation closure then doubles it. Growing the conjugate multiway from the conjugated initial colours and re-quotienting together gives **Q102 = Q51 ∪ C(Q51) = 102 vertices = 51 orig + 51 conj** (zero self-conjugate): ![Closure][4] ## KO-dimension 6 The involution `J` that swaps the two halves is a fixed-point-free permutation with `J² = +I`, and it **anticommutes** with the orig/conj grading `γ` (so `{J, γ} = 0`). Those are exactly the sign data of a real spectral triple of **KO-dimension 6**. Thi is the same KO-dimension the Standard Model's internal space carries in Connes' noncommutative geometry. The notebook checks it directly: ![KO][5] ## The multiway as a derivation graph Every non-seed vertex is produced by composing two parents, so each edge runs from an earlier generation to a later one. Drawn as concentric rings (one per generation), the multiway becomes a derivation graph: 6 seeds at the centre generating a ring of 15, then a ring of 30 and closing at 51. ![DAG Class][6] The full raw multiway (all 456 vertices over five generations) as a derivation mandala (vertices coloured by generation): ![Raw Multiway][7] ## All the gauge sectors on one hypergraph The colour sector gives SU(3). But the full gauge group `[SU(3) × SU(2) × U(1)_Y] × SU(3)_gen` is the **automorphism group of the decoration functor** — derived from closure on the possibilistic layer, not from the NCG bridge (the spectral triple handles anomaly cancellation, not the group). The other sectors ride on the *same* hypergraph as extra fibres; the colour quotient is unchanged: - **SU(2)_weak** — a doublet `w ∈ ℂ²` rotated by an SU(2) element built from the colour cross-product. The weak sector is literally *driven by* colour (it's the stabilizer of the colour output direction). This is the one float layer. - **U(1)_Y** — the residual phase of the weak doublet; not a separate layer. - **SU(3)_gen** — a generation amplitude `g ∈ ℤ[i]³` composing exactly like colour, so its own ray-quotient is a *second, independent* Q51: a decoupled family symmetry. - **ℤ₂ spinor** — a sign `ε` per vertex, the product of its three source signs (the chirality double-cover). ![Sectors][8] Three sectors as fibres on the identical colour-quotient Q51, plus generation as its own parallel quotient. (Unlike exceptional-group "theory of everything" embeddings [cf. **@J Gregory Moxness**'s H₄/E₈ work] here the gauge group is *derived by obstruction*, not embedded in a larger group.) ##A few things to keep straight: - This is an **independent research program** ("Closure Forces Structure"), adjacent to the official Wolfram Physics Project. The shared substrate is hypergraph rewriting; the extra ingredient is Rosen closure. - The notebook **reproducibly verifies the structural facts** (51, 102, the KO-dimension-6 signs, the four gauge-sector decorations). The *forcing arguments* (discrete obstruction, Hurwitz, isotropy, the gauge-group derivation) are theorems in the accompanying paper, not claims the notebook proves by itself. - One layer, the weak doublet, is **float** (an SU(2) rotation with `cos θ`, `sin θ` from `θ = Arg⟨ψ₁|ψ₂⟩`); everything else is exact Gaussian-integer arithmetic. - The object is studied by **observation** (slicing and characterizing the static multiway and its quotients) not by instantiating it as a running dynamical system. ## Run it yourself The attached notebook is self-contained and evaluates top to bottom (≈ a minute; the 456-vertex layout is the slow step). It prints a verification table you can check against the numbers above, then draws every figure in this post including an interactive generation slider: Manipulate[frameAt[G], {{G, 4, "generation"}, 0, 4, 1}] To export the animation: Export["q102_growth.gif", Append[growthFrames, closurePanel], "DisplayDurations" -> 1.2] Comments, criticism, and especially attempts to break it are welcome. &[CFS Notebook][9] --- ##References / related Community posts:* - *Original Reference: Aaron Green (2026). Closure Forces Structure: Rosen Closure and the Standard-Model Algebra. Researchers.One. [https://researchers.one/articles/26.02.00001v7][10]* - *@Ray Aschheim — [WSS21] Color spin networks — https://community.wolfram.com/groups/-/m/t/2311732* - *@Regen Petu-Stiles — [WSS22] Identifying homogeneity in hypergraphs via approximate isomorphism — https://community.wolfram.com/groups/-/m/t/2445699* - *@J Gregory Moxness — The Isomorphism of H₄ and E₈ — https://community.wolfram.com/groups/-/m/t/3073391* ##AI Usage Claude Opus 4.8 (Anthropic) assisted in the drafting of Wolfram code and generation of figures and text used in this post. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=q102_growth.gif&userId=3733286 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_curve.png&userId=3733286 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_frame2.png&userId=3733286 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_closure.png&userId=3733286 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_ko.png&userId=3733286 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_dag_class.png&userId=3733286 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_dag_raw.png&userId=3733286 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig_sectors.png&userId=3733286 [9]: https://www.wolframcloud.com/obj/11f014a0-6090-45bb-994d-68402d1aa461 [10]: https://researchers.one/articles/26.02.00001v7 Aaron Green 2026-06-14T07:06:23Z https://community.wolfram.com/groups/-/m/t/3691199 Hi everyone in the Wolfram Physics / Fundamental Physics Project community, I’ve just finished a 29-page cumulative working document that takes a strictly graph-first approach to electromagnetism, charge, chirality, and family replication. The core is built on a finite oriented graph with compact U(1) links — very much in the spirit of causal graphs and hypergraph models. Quick summary of what’s in the paper: Charge is literally an integer-valued flux-divergence defect on the graph. Exact regional Gauss law, topological quantization from link compactness, exact lattice continuity, Coulomb law from graph-Laplacian minimization, and full Maxwell dynamics emerging in the aligned deconfined phase — all proved cleanly. A common topological language (cellular gauge data + relative current classes + twisted Spinc index theory) unifies charge, chirality, and three-family replication. Explicit finite toy model: product graph $ G = \Lambda_4 \times I_s \times T^2_F $ with domain-wall/overlap fermions and internal flux index 3 gives minimal charge + chirality + three replicated families from one parent generation. Preferred strong ontology (the part I’m most excited about): charged particles are reinterpreted as self-bound local causal shells. A charged lepton is a trapped spinor core coupled to a bosonic shell-deformation sector on a closed 2D simplicial surface. The minimal regular shell is naturally tetrahedral; the leading deformation multiplet is a geometric triplet whose microscopic anisotropy + holonomy collapse to a single-vector operator that automatically produces the exact cosine spectrum used in Koide-type charged-lepton relations. Strong coefficient locking and a codimension-one dynamical balance surface emerge from identical-link tetrahedral geometry and radial-wall tension. The paper is deliberately layered: theorems vs. constructions vs. strong-but-incomplete branches vs. ruled-out ideas. It overlaps structurally with tetrahedral A₄ flavor models but supplies a concrete geometric engine inside the shell rather than abstract flavons. Full PDF (master_working_document_v8.pdf) is attached. Transparency note: I used Grok (xAI) heavily to help me refine the writing, tighten the LaTeX, organize the sections, and make the ideas as clear as possible. The core physics ideas, and ontology are my own — but the AI was instrumental for making this possible. I’d love honest feedback from this community, especially on: how the compact-graph U(1) core and causal-shell picture might connect to hypergraph / causal-graph dynamics, any overlaps or tensions with the Wolfram Physics framework, suggestions for next steps or things I should stress/test. Happy to discuss any part of it. Thanks in advance! Aiden Smith 2026-04-17T01:09:09Z https://community.wolfram.com/groups/-/m/t/3682254 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8239hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/27b9cbf2-47f5-4888-81b8-aa014c78b0c6 Myrto Terpsiadou 2026-04-11T13:27:03Z https://community.wolfram.com/groups/-/m/t/3642808 **Title: Exploring a Finite Multiway System: Exact Computability in the "S21" Discrete Quantum Gravity Model** Hello everyone, I’ve been reviewing a recent theoretical framework called "S21 Theory," and it shares significant conceptual DNA with the Wolfram Physics Project—specifically regarding multiway systems and the emergence of continuous physics from discrete graphs [1, 2]. I thought it would be an interesting model to discuss here, particularly because of how it approaches the problem of infinite state spaces and exact computability. Here is a breakdown of how the S21 model aligns with (and diverges from) the Wolfram approach: **1. The Foundation: A 6-Bit Postulate Instead of Arbitrary Rules** While the Wolfram approach often searches empirically for generative rewriting rules across an infinite space of possible strings [2, 3], S21 derives its structure from a single discrete postulate: spacetime at the Planck scale admits exactly six binary degrees of freedom (bits) per cell [4]. * This 6-bit postulate creates a finite 64-state configuration space (the $Q_6$ hypercube) [5]. * Applying topological consistency and action minimization filters this down to exactly 21 stable configurations [6]. * 20 of these states form a connected visible-sector vacuum manifold ($M_{20}$), while 1 isolated state becomes a Dark Matter candidate ($\sigma$) [6]. **2. Multiway Evolution and Exact Solvability** S21 explicitly utilizes the multiway evolution paradigm [1]. Dynamics in the S21 vacuum occur as a multiway directed acyclic graph (DAG) where the system simultaneously explores all allowed paths on a 20-node physical transition graph ($G_E$) [7]. * **The "Wolfram Difference":** The S21 author explicitly compares the two models, noting that because S21 is restricted to a finite 20-state manifold rather than an infinite state space, its multiway evolution is *exactly solvable* [2, 3]. * The discrete Feynman path integral (summing over all paths in the multiway graph) is evaluated exactly, matching matrix-inverted Green's functions to machine precision ($10^{-14}$) [8]. This provides a convergent, explicit sum without the need for Monte Carlo approximations or dealing with divergent infinities [9]. **3. Emergent Curvature (Ollivier-Ricci)** Just as Wolfram models look for continuum limits of discrete hypergraphs, S21 proves that continuous relativistic geometry emerges from the discrete graph $G_E$. By computing the Ollivier-Ricci curvature using optimal transport (Wasserstein-1 distance) between the neighborhoods of adjacent vertices, the theory proves the graph has a uniform negative curvature ($\kappa = -1/3$) [10, 11]. This establishes the vacuum as a constant-curvature homogeneous space satisfying the discrete Einstein equations [12]. **4. Topological Origin of the Standard Model** Instead of treating particle physics as an add-on, S21 claims the Standard Model is structurally inevitable from the graph topology: * **Fermion Generations:** The topological skeleton of the 20-state manifold has a first Betti number of $b_1 = 3$, which exactly matches the 3 generations of fermions [13]. * **Particle Spectrum:** The 43 "forbidden" states ($F_{43}$) outside the vacuum manifold act as an encoding space for the particle spectrum. The boundary membrane between the forbidden sector and the vacuum yields exactly 39 observable states (1 Higgs + 12 gauge bosons + 16 quarks + 10 leptons), which perfectly divides into 13 particles across 3 generations [14, 15]. * **Cosmology:** The framework tracks the minimal CP-odd closed walk on the graph, finding a length of $l_{min} = 7$ [16]. This single integer invariant is used to derive both the baryon asymmetry ($\sim 10^{-10}$) and the cosmological constant ($\sim 10^{-119}$) [17, 18]. **Discussion Prompt for the Forum:** The S21 framework suggests that by restricting a multiway system to a highly constrained, finite topological manifold ($M_{20}$), we can bypass the computational intractability of infinite state spaces and extract exact, quantitative cosmological parameters [2, 3]. Has anyone here experimented with similarly constrained, finite multiway systems? I’d be very interested in hearing the community's thoughts on using a strictly finite 6-bit partition to solve the path integral convergence problem in discrete quantum gravity. Suhail Bachani 2026-02-21T00:32:44Z https://community.wolfram.com/groups/-/m/t/3631121 I am working on a model that requires a specific type of "Selection Bias" in the rule evolution, and I am looking for guidance on how to represent this using WolframModel or MultiwaySystem. The Theoretical Goal: I am trying to simulate a "stabilization" phase where the system transitions from a high-entropy state (random fluctuations) to a structured state (durable causal loops). I hypothesize that this requires a Parity-Breaking Bias (which I call "The Twist") that weights the path integral. The Mechanism I Want to Model: Instead of all branches in the Multiway System having equal weight, I want to penalize branches that are "topologically symmetric" and reward branches that exhibit a specific "Chiral Asymmetry" (Twist). >Hypothesis: This bias should force the Causal Graph to "lock" into durable subgraphs (particles/structures) rather than exploring the full infinite Ruliad. The Question: Is there a standard way in WolframModel to apply a "Selection Function" or "Path Weight" that prunes the Multiway Graph based on the topological properties of the hypergraph at that step? Context: This is part of a larger framework ("Universal Compression") linking causal graph dynamics to observer constraints. >System Architecture (Preprint): https://doi.org/10.5281/zenodo.18421925 >Specific Cosmological Derivation: https://doi.org/10.5281/zenodo.18421691 Any pointers on how to implement a "Selection Bias" function in the evolution step would be appreciated. Matt Prager 2026-01-30T11:29:43Z https://community.wolfram.com/groups/-/m/t/3580238 I’ve been thinking about how the Wolfram model treats manifold-like behavior as an emergent, approximate property of the underlying hypergraph. In regions of extreme causal-edge density — for example near black hole interiors — the manifold approximation is expected to break down. My question is this: When the manifold structure collapses, does the distinction between different effective “universes” (different limiting foliations or rule-equivalence classes in the Ruliad) also collapse? In other words, if spatial distance and branchial distance both arise from constraints on causal reducibility, then in a region where those constraints fail (because the updating is too dense or too singular), do previously distant parts of branchial space become adjacent? The speculative idea is that a black hole interior might serve as a region where manifold structure, branchial separation, and even differences between emergent effective laws of physics lose their usual distinctions, because the underlying hypergraph is no longer well-approximated by any smooth foliation. Could this imply that a black hole is a nexus where different emergent universes in the Ruliad could become computationally adjacent in ways they normally aren’t, like an *even more* speculative variation on a wormhole? A bridge entangling parts of the Ruliad whose physics don't even look the same? I’m wondering whether anything in the current WPP formalism supports or contradicts this possibility, but this is well outside my area of study. If anyone deep into the Wolfram Physics Project has explored this rather sci-fi notion, I would be grateful to hear their musings! Brenden Martin 2025-11-22T20:03:09Z https://community.wolfram.com/groups/-/m/t/3299868 Visually intriguing 2D animations of randomly found Wolfram Physics Models. There is a model finder file for random scans, and some example files of "things found", like the moebishWorm, the wapeTorm, and others named and unnamed. Anyone know of a way to show that a given {{3,4}->{7,4}}, or more complex model, is equivalent to a simpler model (say, {{2,3}->{3,3}}? Marcos Ferrer 2024-10-17T07:24:50Z https://community.wolfram.com/groups/-/m/t/3036786 I am doing a bit of research in Wolfram Physics model and I would like to include this in a blog about pop-science. There is a section about the "Research Network" where I would like to indicate the persons involved in this project and all the countries where they have worked (not only necessarily their country of origin). There are two countries that I have found some fuzzy indications that some people involved in the Wolfram Physics Project have worked in them. These are Hungary and Lithuania. However, I have not been able to find anything clear. Despite being a somewhat strange question, are there any people involved in the Wolfram Physics Project that have worked or studied in Hungary or Lithuania at any point of their careers? Nodu Agga 2023-10-16T13:29:48Z https://community.wolfram.com/groups/-/m/t/2986471 I'm interested to learn more about what ideas and work has been done with respect to Lagrangian / principle of least action etc. with respect to the Wolfram Physics Project; it is mentioned in Chapter 8 of the Technical Introduction, but I'm wondering if anyone knows of any "further reading" of sorts on this topic. Thanks! Quote from Chapter 8.3: "quantum action density (Lagrangian): total flux (divergence) of multiway causal graph edges". I would be very curious to understand the derivation or connection. Robert Mendelsohn 2023-08-08T16:28:13Z https://community.wolfram.com/groups/-/m/t/2972606 I would like to mention a word at this moment - "Aether." If anyone feels uncomfortable with this word, kindly refrain from reading further. Wolfram is a powerful tool that can manipulate geometric shapes and create new units of measurement. However, it lacks a fundamental physics paradigm based on geometry and a comprehensive unit system that can make understanding fundamental physics as intuitive as Classical Mechanics. I have dedicated more than two decades to creating a revolutionary physics system that leads us back to the concept of Aether, which was wrongly discarded in the early 1900s. I've authored a book on this topic, which can be accessed for free at sota.aetherwizard.com. This new approach enables a simple Unified Force Theory based on Newtonian force laws, while also quantifying Einstein's General Relativity equations in terms of matter-Aether tensors. Moreover, this physics system introduces new units of measurement based on distributed charge and two different types of charges: electrostatic and magnetic. It is significant to note that space can be measured as a quantum structure that includes geometry and spin. We can even create a model of space using five dimensions that is easily understandable for high school students. This model helps us understand the structure of subatomic particles and how matter interacts with space (Aether). This forum aims to quantify fundamental physics in significant ways, and I possess the crucial concepts that can facilitate this goal. However, mainstream academia seems to hold a significant irrational bias towards the concept of quantum and fluid space. This should not be the case because it is precisely what Henri Poincare and Hendrik Lorentz were quantifying when they developed the Lorentz transformations. Furthermore, Albert Einstein's General Relativity theory unintentionally presents a powerful fluid Aether theory as well. I have a fixed income and only possess a GED high school diploma, but I have spent the last forty years reading books and scientific papers. Unfortunately, my severe hearing loss prevents me from engaging in meaningful voice conversations. Despite this, I have no intention of selling anything, asserting authority, or belittling anyone. I have simply discovered some highly practical and straightforward physics concepts using ideas that others discarded over a century ago. I am seeking open-minded individuals who value functional ideas over diplomas on a wall. My goal is to enhance my visual aids to help others better understand new concepts in physics. I aim to create new physics calculators that focus on dimensional analysis, reducing the reliance on abstract calculus and leading to less abstract paradigms. Is there anyone present who is open to giving a new idea a fair chance? David Thomson 2023-07-20T20:56:06Z https://community.wolfram.com/groups/-/m/t/2840833 The question "[What is the shortest description of a universal computational structure that includes a meta-circular evaluator?][1]" gives rule 110 as an example of a short rule that is incapable of short homoionic (meta-circular) description. This is important as it provides closure on Kolmogorov Complexity's choice of UTM. This is a different *kind* of question than asking, "What is the UTM with the shortest description?" Restating the question in computerdom vernacular: What is the shortest known program that simulates the Universal Computation machine on which it runs? In other words, the program is an interpreter that if you feed it a binary to execute, will produce exactly the same result as if you had fed the binary to the machine directly. This would seem to overcome a (rather pedantic IMHO) objection to Algorithmic Information approximation as the most principled information criterion for model selection: That the choice of instruction set is arbitrary. As such it would seem to be an appropriate prize challenge running in parallel to the Hutter Prize and for similar reasons. PS: In the few online conversations on this question I've run across since 2002, there are various games one can play to try to evade this question such as arise when people talk about the combinatorial calculus (SK combinators) or other concatenation formal languages as requiring descriptions external to their physical implementation. To these objections I can respond with my original suggestion to Hutter which was that to whatever level of abstraction of the physical one may wish to take as "real", there is still the challenge of simulating that level of physical abstraction as the substratum of universal computation. So pick your level. NOR gates? Maxwell’s equations? QED? The point is that these are *not arbitrary*. [1]: https://cstheory.stackexchange.com/questions/34879/what-is-the-shortest-description-of-a-universal-computational-structure-that-inc James Bowery 2023-02-28T13:44:54Z https://community.wolfram.com/groups/-/m/t/2677088 I have a few questions about Wolfram's theory for fundamental physics that I would like to clarify... I. First, as I understand it, and please correct me if I'm wrong, is that similar observers to us will most likely perceive at least the same "general laws" (or most fundamental laws) of physics and mathematics. But for vastly different observers compared to us, couldn't they be able to perceive vastly different general laws? II. Recently, Stephen Wolfram wrote an interesting article about his proposed relationship between maths and physics (https://writings.stephenwolfram.com/2022/03/the-physicalization-of-metamathematics-and-its-implications-for-the-foundations-of-mathematics/#some-historical-and-philosophical-background). There, Wolfram talks about the physicalization of mathematics and adopts some sort of platonic position saying that mathematics does really exist in some sense or another because mathematics and all the relations between abstract concepts would exist in the ruliad (more information in the article). This reminded me of Tegmark's thesis of the "Mathematical Universe Hypothesis" (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) where all mathematical structures would exist as separated universes. (There's even a comment in that article asking what is the relation between Wolfram's and Tegmark's ideas, but nobody replied). Therefore, basically my question is: Since Wolfram says that mathematical concepts and structures would exist in the ruliad, and the rulial space is what makes reality (and every possibility is realized by it), couldn't we say that all the universes proposed by Tegmark would exist in some way according to Wolfram's ideas? Couldn't all logically possible worlds exist in some way according to this? Nodu Agga 2022-10-29T01:52:30Z https://community.wolfram.com/groups/-/m/t/2634961 How should we think about the amplituhedron wrt to the Wolfram physics project? Are the two hypotheses compatible? Could the amplituhedron tell us something about the properties of the underlying graph? Patrick Arnesen 2022-10-05T18:24:06Z https://community.wolfram.com/groups/-/m/t/2611614 Hello, my name is Spencer Hargiss, I'm new here. I just remembered an idea I had when learning about the Wolfram Physics project, and it still seems exciting to me. It lacks mathematical rigor, but might be useful. And I thought, hey, why not share? The idea is that maybe the universe isn’t a graph, but is a self-replicating pattern of information within a graph. I’m going to try to make an argument for why it’s worth taking this possibility seriously. The possibility could change our ideas about what kind of graph we are looking for, and alter basic assumptions about how the graphs relate to quantum mechanics. And in any case, it's a delicious idea and great brain-candy, so it's probably worth chewing on as food for thought. The inflationary universe, in most theories I’ve heard of, expanded unbelievably fast… within a truly microscopic period of time it became so large that nobody really knows how big it is. Yet, right after that things settled down, and now it’s expanding at a measurable, accelerating, but pretty modest rate. That’s a massive discrepancy. It reminds me of the difference between the strength of the gravitational force and the other forces, the difference in magnitude is so large. It screams for an explanation. Let’s say the graph tends to expand at some sort of rate, let’s say every step the number of nodes doubles. If a step corresponds to the Planck length or something like that, that’s going to be a really unbelievable expansion rate. Every second the universe would get 2^10^44 something times bigger… that’s just a crude non-rigorous ballpark estimate. The point is it might account for the blistering rate of expansion in the early universe. That might suggest, when figuring out what hyper graph rule we’re looking for, we should look for a rapidly expanding rule like that. If the Universe is based on cellular automata like rules and has that kind of Oomph, the oomph must emerge from the rule itself. But then what happened? Why is the universe not expanding at that rate if it's driven by a rule which tends to do that? I'm sure there's lots of explanations out there already in the community, and I wouldn't doubt someone's already considered the one I'm going to propose. The idea is that the universe is not simply the graph, but a self-replicating pattern inside the graph. Kind of like a cellular automation on a strand of DNA… the pattern is a 1D pattern, but it replicates into a higher dimensional space. You could imagine DNA that doesn’t copy exactly but instead follows a rule, like a classic cellular automata rule. Each time it’s copied, time advances one step on the DNA. Any creatures that exist in this DNA automation universe would experience themselves as occupying a 1D universe which is changing in size relatively slowly, even as the pattern really grows geometrically. If they looked really closely at things they might find evidence of the copying process which could clue them in. Similarly, you can imagine a rapidly expanding graph being the agar or substrate in which a 3D pattern—the universe—is replicating itself, and evolving according to a 3D rule which is distinct from the graph rule. The graph itself could be 3D (each node on average connecting to 6 others, or whatever), but it's likely to have more dimensions than the pattern. The process of replication could be much simpler than the process for biological organisms, since it exists on a much simpler level and doesn't have metabolism or competition to deal with. This idea could range from a weak version where copying information is simply what this graph rule does from the start, or a strong version where the copying process evolved through a messy drawn out process of natural selection, in which the 'natural laws' we know are the product of evolution and adaptation seeking to maximize the rate of replication. Remember that the graph evolves so rapidly and is so large that if the emergence of a replicator is even possible at that level, it would come about much more quickly and inevitably than with biological life. This way we could still imagine that the graph has a rapidly expanding rule, and also explain our slowly expanding universe. I could say a lot more, but all of this is completely conceptual rather than mathematical, I'm going to treat this post as a seed which I hope might sprout into a real hypothesis in a more methodical mind than my own. Thanks for reading! Anyone who has any questions, comments, or objections: please let me know. Spencer Hargiss 2022-09-05T17:53:06Z https://community.wolfram.com/groups/-/m/t/2485244 Does the Physics Project support Genetic Algorithms -- Selection, Cross-over and Mutation? benorden 2022-03-05T04:36:50Z https://community.wolfram.com/groups/-/m/t/2432307 In Wolfram’s and Gorard’s papers (https://arxiv.org/abs/2004.08210 and https://arxiv.org/abs/2004.14810), general relativity was derived from Wolfram models. But what is the improvement over the famous Seth Lloyd’s ‘quantum gravity from computation’ paper, which involved deriving general relativity from computational graphs and computational histories?: https://arxiv.org/pdf/quant-ph/0501135.pdf Regarding general relativity, has the Wolfram physics project uncovered something that Seth Lloyd had not previously uncovered? John Johnson 2021-12-25T15:17:18Z https://community.wolfram.com/groups/-/m/t/2431784 In Wolfram’s and Gorard’s papers (https://arxiv.org/abs/2004.08210 and https://arxiv.org/abs/2004.14810), the claim seems to be that Lorentz symmetry/invariance/covariance automatically follows from causal invariance. However, what they mean with Lorentz symmetry seems to refer to a much weaker property, since there is no Lorentz group O(1,3) appearing in their paper. Regarding special relativity, If there is no true Lorentz symmetry from Wolfram models, then is there any real improvement over the pre-existing causal set theory? John Johnson 2021-12-25T05:46:31Z https://community.wolfram.com/groups/-/m/t/2380863 Are the four paradigms of science described in this Stephen Wolfram's writing (https://writings.stephenwolfram.com/2021/09/even-beyond-physics-introducing-multicomputation-as-a-fourth-general-paradigm-for-theoretical-science/) more general as we reach the 4th paradigm of the 2020's? In other words, does the 4th paradigm (the multi computational one) englobe or include the rest of them? Is it a "generalization" of all of them? (I mean, mathematical models are not included in the first "structural" paradigm, since they usually consider time, while in the structural paradigm time is not considered. But the mathematical paradigm includes all the models from the structural paradigm, since time is or is not considered in mathematical models. So, would this continue up until the last paradigm, which would include all the models from the rest)? If it is, then, according to the framework of the multicomputational paradigm, every possible model from the rest paradigms (all possible structural, mathematical and computational models) would be included in it. But if that is really the case, then, how could there be an incompatible model with Wolfram's framework (which is basically the multicomputational one) as he says here ( https://www.wolframphysics.org/questions/scientific-general-interest/ ): > Any particular rule could be proved wrong by disagreeing with > observations, for example predicting particles that do not exist. But > the overall framework of our models is something more general, and not > as directly amenable to experimental falsification. Asking how to > falsify our framework is similar to asking how one would prove that > calculus could not be a model for physics. An obvious answer would be > another model successfully providing a fundamental theory of physics, > and **being proved incompatible**. If his multicomputational framework englobes every possible conceivable model, how can there be any model incompatible with it? Nodu Agga 2021-10-06T23:21:02Z https://community.wolfram.com/groups/-/m/t/2349536 We show a Wolfram model whose renormalization generates a sequence of approximations of a wave function having the Pauli-x matrix as Hamiltonian. [Preprint][1] [1]: https://arxiv.org/pdf/2108.08300.pdf José Manuel Rodríguez Caballero 2021-08-23T04:30:44Z