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A number of substantive edits have been introduced from the prior version. These expand considerably on the prior commentary on the general construction of Wolfram's theory, its espoused benefits, and the criticism it has received.

In April 2020, Wolfram announced the "Wolfram Physics Project", an effort to develop a general framework for unifying and explaining previously disparate laws of physics[1]. In particular, Wolfram's framework distinguishes itself for its capacity to simultaneously reproduce "space, time, relativity, gravity and hints of quantum mechanics[2]." Its emphasis on uniting the latter two phenomena has led to the project being broadly cited as introducing a potential theory of everything[3]. Developing on ideas first articulated in A New Kind of Science, Wolfram's paradigm re-orients physical principles as effectively extending from observed phenomena of hypergraphs transformed by iterative application of minimal rewriting rules that obey the Church–Rosser property (i.e. the order in which reduction rules are applied doesn't matter)[4].

Critically, Wolfram's project does not stake its value on a present possibility for directly describing phenomena in the universe as such. Wolfram has thus far made no claim to having found a particular combination of starting conditions or rewriting rules which can be said to adequately simulate any observed physical phenomena. Rather, Wolfram generally stakes the value of his project on two bases. First, the capacity for the progressive transformation of hypergraphs, models selected for being "as minimal and structureless and possible", to produce exceptionally rich, complex structures often broadly reminiscent of physical phenomena[5]. This notion has been a persistent theme in Wolfram's research career and was the subject of significant exposition in A New Kind of Science (see above). Second, Wolfram offers that if any "simple model" does exist, previous conceptions on which prior theories of the universe have been based, notably "notions like space and time", will cease to be of direct relevance to furthering human understanding of the universe[6].

In order to make sense of a particular rule being applied in a given instance, Wolfram's program introduces the concept of rulial spaces. Broadly inspired by frames of reference as understood in special relativity, whereby a particular rule is "selected" only insofar as the observed development of a hypergraph is explicable by a particular rule in a given frame of reference. From this vantage point, in a given system all possible rules have always been applied to lead a hypergraph to its observed state[7]. Causal invariance in the application of reductive rules due to the Church-Rosser property by which one can reconstruct the underlying behavior of a hypergraph allow for the existence of multiple simultaneously valid frames of reference[8]. As a further generalization of rulial spaces, Wolfram introduces the ruliad. Whereas to form a given rulial space one considers a given starting hypergraph and all possible rules which may be used to transform said hypergraph up to a particular end point, the ruliad consists of all possible rules for transforming a given hypergraph applied in all possible ways simultaneously. Wolfram finds this a sufficient articulation of general computational possibilities. Given this conceptual broadness, Wolfram does not consider the ruliad neatly expressible as a mathematical concept per se, it being better understood as a metamathematical object expressing all mathematical theories simultaneously[9].

Wolfram's claims have been met with generally chilled response from the broader physics and computation communities. Criticisms include the current lack of predictive power in Wolfram's theory as well as notable gaps in the theory's reproduction of physical phenomena. Theoretical computer scientist Scott Aaronson has been an especially vocal critic of Wolfram's project, describing Wolfram's incorporation of established physical into his model as essentially tautological: "If we suppose that a rabbit was coming out of the hat, then remarkably, this rabbit would be coming out of the hat[10]." Some have even gone to suggest that the aim of developing fine computational models for use in various scientific disciplines not limited to physics is in deep contradiction with his principle of computational irreducibility[11]. Further criticism has been leveled at Wolfram's self-segregation from the broader scientific community, developing his ideas without the opportunity for significant dialogue beyond a small group of collaborators or the scrutiny of peer review. These have been interpreted as especially perverse given Wolfram's wealth and combination of gender and racial backgrounds (especially as are in conformation with the "trope of the solitary, white, male genius") potentially affording him an unduly privileged position in scientific dialogues[12]. Responding to such criticisms Wolfram has generally offered key features of his program - e.g. the emergence of physical phenomena from extremely simple computational models - as sufficient rebuttal, complaining on the "naiveté" of many objections as posed to him[13].

Original Version:

In April 2020, Wolfram announced the "Wolfram Physics Project" as an effort to reduce and explain all the laws of physics within a paradigm of a hypergraph that is transformed by minimal rewriting rules that obey the Church–Rosser property. The effort is a continuation of the ideas he originally described in A New Kind of Science. Wolfram claims that "From an extremely simple model, we're able to reproduce special relativity, general relativity and the core results of quantum mechanics."

Physicists are generally unimpressed with Wolfram's claim, and say his results are non-quantitative and arbitrary.

  1. ^ Wolfram, Stephen (2020-04-14). "Finally We May Have a Path to the Fundamental Theory of Physics… and It's Beautiful". Stephen Wolfram Writings.
  2. ^ Wolfram, Stephen (2020-04-14). "Finally We May Have a Path to the Fundamental Theory of Physics… and It's Beautiful". Stephen Wolfram Writings.
  3. ^ Becker, Adam (2020-08-01). "Physicists Criticize Stephen Wolfram's 'Theory of Everything'". Scientific American. Retrieved 2025-05-25.
  4. ^ Wolfram, Stephen (2020-04-14). "Finally We May Have a Path to the Fundamental Theory of Physics… and It's Beautiful". Stephen Wolfram Writings.
  5. ^ "Wolfram Physics Project | A Class of Models with the Potential to Represent Fundamental Physics". www.wolframphysics.org. Retrieved 2025-05-25.
  6. ^ Wolfram, Stephen (2020-10-05), A Class of Models with the Potential to Represent Fundamental Physics, arXiv, doi:10.48550/arXiv.2004.08210, arXiv:2004.08210, retrieved 2025-05-25
  7. ^ "Exploring Rulial Space: The Case of Turing Machines—Wolfram Physics Bulletins". bulletins.wolframphysics.org. 2020-06-09. Retrieved 2025-05-26.
  8. ^ "The Phenomenon of Causal Invariance: Wolfram Physics Project Technical Background". www.wolframphysics.org. Retrieved 2025-05-26.
  9. ^ Wolfram, Stephen (2021-11-10). "The Concept of the Ruliad". Stephen Wolfram Writings.
  10. ^ Becker, Adam (2020-08-01). "Physicists Criticize Stephen Wolfram's 'Theory of Everything'". Scientific American. Retrieved 2025-05-25.
  11. ^ "Why Stephen Wolfram's research program is a dead end - SingleLunch". singlelunch.com. Retrieved 2025-05-25.
  12. ^ Mandelbaum, Ryan F. (2020-04-22). "The Trouble With Stephen Wolfram's New 'Fundamental Theory of Physics'". Gizmodo. Retrieved 2025-05-25.
  13. ^ Becker, Adam (2020-08-01). "Physicists Criticize Stephen Wolfram's 'Theory of Everything'". Scientific American. Retrieved 2025-05-25.

Peter's Feedback

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The in-line feedbacks are bolded with [ ], and I use strikethrough to suggest removal of text.

General feedback: The article is rich in information, and provides much more detailed exposure to the Wolfram physics project and the critiques than the original post.

I find the writing made the article a little hard to follow. Quite a few sentences have long and complicated structures. I would suggest some grammatical editions. And please forgive me for making some grammatical editions, and these editions may be unnecessary or even problematic.

There are abundant references! While a large amount of them are primary source of Wolfram's paper, it is understandable as he is probably one of the few supporters of his own theory. At some places, the article stated Wolfram's claims in an objective tone, which I suggest to be framed with "proposed, claimed, indicated..'' as the theory is far from being accepted by academia.


In April 2020, Wolfram announced the "Wolfram Physics Project", an effort to develop a general framework for unifying and explaining previously disparate laws of physics[1]. In particular, Wolfram's framework distinguishes itself for its [proposed] capacity to simultaneously reproduce "space, time, relativity, gravity and hints of quantum mechanics[2]." Its emphasis on uniting the latter two phenomena has led to the project being broadly cited as introducing a potential theory of everything[3]. Developing on ideas first articulated in A New Kind of Science, Wolfram's paradigm [claims to] re-orients physical principles as effectively extending from observed phenomena of hypergraphs transformed by iterative application of minimal rewriting rules that obey the Church–Rosser property (i.e. the order in which reduction rules are applied doesn't matter)[4].

Critically, Wolfram's project does not stake its value on a present possibility for directly describing phenomena in the universe as such. Wolfram has thus far made no claim to having found a particular combination of starting conditions or rewriting rules which can be said to adequately simulate any observed physical phenomena. Rather, Wolfram generally stakes the value of his project on two bases. First, the capacity for the progressive transformation of hypergraphs, [the model] models selected for being "as minimal and structureless and possible", [allows the production of]to produce exceptionally rich, complex structures often broadly reminiscent of physical phenomena[5]. This notion has been a persistent theme in Wolfram's research career and was the subject of significant exposition in A New Kind of Science (see above). Second, Wolfram offers that if any "simple model" does exist, previous conceptions on which prior theories of the universe have been based, notably "notions like space and time", will cease to be of direct relevance to furthering human understanding of the universe[6]. [I find myself confused at this sentence, and understand the reference's original sentence a bit better. I found the original sentence in your reference, which says that

Our approach here is to carry out a fairly extensive empirical investigation of the models, then to use the results of this to make connections with known mathematical and other features of physics. We do not know a priori whether any model that we would recognize as simple can completely describe the operation of our universe—although the very existence of physical laws does seem to indicate some simplicity. But it is basically inevitable that if a simple model exists, then almost nothing about the universe as we normally perceive it— including notions like space and time—will fit recognizably into the model.

I think the point here is not that the previous conceptions will be irrelevant to furthering human understanding in a simple model, but that "if a simple model describing the universe exists, then human's conception will not be in accordance with what the model describes."]

In order to make sense of a particular rule being applied in a given instance, Wolfram's program introduces the concept of rulial spaces. Broadly inspired by frames of reference as understood in special relativity, whereby a particular rule is "selected" only insofar as the observed development of a hypergraph is explicable by a particular rule in a given frame of reference. From this vantage point, in a given system all possible rules have always been applied to lead a hypergraph to its observed state[7]. Causal invariance in the application of reductive rules due to the Church-Rosser property by which one can reconstruct the underlying behavior of a hypergraph allow for the existence of multiple simultaneously valid frames of reference[8]. As a further generalization of rulial spaces, Wolfram introduces the ruliad. Whereas to form a given rulial space one considers a given starting hypergraph and all possible rules which may be used to transform said hypergraph up to a particular end point, the ruliad consists of all possible rules for transforming a given hypergraph applied in all possible ways simultaneously. Wolfram finds this a sufficient articulation of general computational possibilities. Given this conceptual broadness, Wolfram does not consider the ruliad neatly expressible as a mathematical concept per se, it being better understood as a metamathematical object expressing all mathematical theories simultaneously[9].

Wolfram's claims have been met with generally chilled response[this is slightly informal. Probably consider the term provoke skeptism widely among scholars?] from the broader[Does he have supporters in the community of a particular subfield of physics? If not, then probably just say physics community instead of broader physics. If so, probably add the information to the article?] physics and computation communities. Criticisms include the current lack of predictive power in Wolfram's theory as well as notable gaps in the theory's reproduction of physical phenomena. Theoretical computer scientist Scott Aaronson has been an especially vocal critic of Wolfram's project, describing Wolfram's incorporation of established physical into his model as essentially tautological: "If we suppose that a rabbit was coming out of the hat, then remarkably, this rabbit would be coming out of the hat[10]." Some have even gone to suggest that the aim of developing fine computational models for use in various scientific disciplines not limited to physics is in deep contradiction with his principle of computational irreducibility[11]. Further criticism has been leveled at Wolfram's self-segregation from the broader scientific community, developing his ideas without the opportunity for significant dialogue beyond a small group of collaborators or the scrutiny of peer review. These have been interpreted as especially perverse [the word perverse is quite non-objective and value laden; perhaps should be avoided on wiki] given Wolfram's wealth and combination of gender and racial backgrounds potentially affording him an unduly privileged position in scientific dialogues[12]. Responding to such criticisms Wolfram has generally offered key features of his program - e.g. the emergence of physical phenomena from extremely simple computational models - as sufficient rebuttal, complaining on the "naiveté" of many objections as posed to him[13].

Evan Cholerton Peer Review

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I really enjoyed diving into your write-up on the Wolfram Physics Project. You’ve pulled together some fascinating details, but right now it reads more like a research essay than a Wikipedia article. I would suggest opening with a snappy summary that states what the Project is and why it matters, and breaking your content into sections.

I noticed a few moments where the language turns lofty. You might swap in more neutral wording and tighten sentences to one idea each. Finally, don’t forget to italicize titles like A New Kind of Science and link key terms.

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