Wolfram Model - Revision history

LukeW: LukeW moved page Wolfram Model Training Course to Wolfram Model

2025-08-20T15:05:25Z

LukeW moved page Wolfram Model Training Course to Wolfram Model

← Older revision		Revision as of 15:05, 20 August 2025
(No difference)

LukeW: /* Complex Systems */

2025-07-31T02:58:51Z

Complex Systems

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	Before diving into the work of Stephen Wolfram, the Wolfram Physics Project, or most projects from the Wolfram Institute, it's helpful to have some background knowledge in certain fields and concepts. If you're unfamiliar with these terms, below are some helpful video links and concise definitions.		Before diving into the work of Stephen Wolfram, the Wolfram Physics Project, or most projects from the Wolfram Institute, it's helpful to have some background knowledge in certain fields and concepts. If you're unfamiliar with these terms, below are some helpful video links and concise definitions.

	=== ~~[https://www.youtube.com/watch?v=vp8v2Udd_PM~~ Complex Systems] ===		=== Complex Systems ===
	A basic introduction to complexity theory, covering network graphs and how those are used to model systems.		A basic introduction to complexity theory, covering network graphs and how those are used to model systems. For a good introduction to complex systems, watch [https://www.youtube.com/watch?v=vp8v2Udd_PM What is a Complex System?] on YouTube.

	=== [https://www.youtube.com/watch?v=ZPbYriK_gCs Isomorphism] & [https://www.youtube.com/watch?v=hVerxuP4cFg Graph Isomorphism]===		=== [https://www.youtube.com/watch?v=ZPbYriK_gCs Isomorphism] & [https://www.youtube.com/watch?v=hVerxuP4cFg Graph Isomorphism]===
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	[https://www.youtube.com/watch?v=gM6yb4E9wK0 Nima Arkani Hamed: 1/n (April 17, 2025)]		[https://www.youtube.com/watch?v=gM6yb4E9wK0 Nima Arkani Hamed: 1/n (April 17, 2025)]

	== ~~Notes~~ ==		== References ==

LukeW at 02:49, 31 July 2025

2025-07-31T02:49:00Z

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	== '''~~Part 3 :~~ The Ruliad''' ==		== '''The Ruliad''' ==

	The work of A New Kind of Science and the Principle of Computational Equivalence tells us that systems can emulate each other's behavior and, therefore, all perform computations as sophisticated as any other arbitrarily complicated system, which also makes them as sophisticated as a Turing universal machine. In some sense, we can state colloquially that all systems are just this single Turing machine.		The work of A New Kind of Science and the Principle of Computational Equivalence tells us that systems can emulate each other's behavior and, therefore, all perform computations as sophisticated as any other arbitrarily complicated system, which also makes them as sophisticated as a Turing universal machine. In some sense, we can state colloquially that all systems are just this single Turing machine.
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	=== [https://writings.stephenwolfram.com/2021/04/why-does-the-universe-exist-some-perspectives-from-our-physics-project/#the-laws-of-the-rulial-universe Why Does the Universe Exist? Some Perspectives from Our Physics Project—Stephen Wolfram Writings] ===		=== [https://writings.stephenwolfram.com/2021/04/why-does-the-universe-exist-some-perspectives-from-our-physics-project/#the-laws-of-the-rulial-universe Why Does the Universe Exist? Some Perspectives from Our Physics Project—Stephen Wolfram Writings] ===

	== '''~~Part 4 :~~ Observation & Observer Theory''' ==		== '''Observation & Observer Theory''' ==

	The properties of the Ruliad elicit another series of questions about how it can be perceived. That because, any subsystem of the Ruliad can only map surjectively onto it, then any subsystem that exists anywhere inside of this object will consolidate information about its structure.		The properties of the Ruliad elicit another series of questions about how it can be perceived. That because, any subsystem of the Ruliad can only map surjectively onto it, then any subsystem that exists anywhere inside of this object will consolidate information about its structure.
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	=== [https://www.youtube.com/watch?v=VDGyZUfL1BA Stephen Wolfram on Observer Theory] ===		=== [https://www.youtube.com/watch?v=VDGyZUfL1BA Stephen Wolfram on Observer Theory] ===

	== '''~~Part 5 :~~ The Wolfram Model''' ==		== '''The Wolfram Model''' ==

	With New Kind of Science, The Ruliad and Observer Theory under your belt, you are now prepared and properly equipped to understand the weight and importance of the Wolfram Model.		With New Kind of Science, The Ruliad and Observer Theory under your belt, you are now prepared and properly equipped to understand the weight and importance of the Wolfram Model.
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	== '''~~Part 7 :~~ Multi-Computation''' ==		== '''Multi-Computation''' ==

	If one takes the idea of Computational Equivalence to its logical conclusion, then Ruliology, the study of rules, ultimately means that what every rule does is essentially “everything” since all rules are computationally equivalent to that of a Turing Universal Machine. For Ruliology, it isn’t meaningful to write on each page of the aforementioned encyclopedia that every rule “does everything.” This is where Multi-computation steps in to provide operational meaning to Ruliology and a more powerful way to think about and exploit the properties of this framework to model systems, create technology and do science.		If one takes the idea of Computational Equivalence to its logical conclusion, then Ruliology, the study of rules, ultimately means that what every rule does is essentially “everything” since all rules are computationally equivalent to that of a Turing Universal Machine. For Ruliology, it isn’t meaningful to write on each page of the aforementioned encyclopedia that every rule “does everything.” This is where Multi-computation steps in to provide operational meaning to Ruliology and a more powerful way to think about and exploit the properties of this framework to model systems, create technology and do science.
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	Time Stamp 1:38:43 - 1:38:53		Time Stamp 1:38:43 - 1:38:53

	== '''~~Part 8 :~~ Impact''' ==		== '''Impact''' ==

	The Wolfram Model has an unprecedented impact on a multitude of areas, far beyond just physics. From Philosophy, to Economics, Biology, and Graphics Programming... Like stated in Section 5, and as we will again state below, in principle all systems can be modeled as Wolfram Models, or at least be meaningfully described in this framework. So take the initiative and apply the framework to your own fields of study, or research area, and see how they might apply there. In this step, we provide just a few of the implications to get you started.		The Wolfram Model has an unprecedented impact on a multitude of areas, far beyond just physics. From Philosophy, to Economics, Biology, and Graphics Programming... Like stated in Section 5, and as we will again state below, in principle all systems can be modeled as Wolfram Models, or at least be meaningfully described in this framework. So take the initiative and apply the framework to your own fields of study, or research area, and see how they might apply there. In this step, we provide just a few of the implications to get you started.
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	The Wolfram Model implies that science is an exploration of an infinite landscape, similar to art we just create the things that we want to create. That doing science is an exercise in programming the universe.		The Wolfram Model implies that science is an exploration of an infinite landscape, similar to art we just create the things that we want to create. That doing science is an exercise in programming the universe.

	== '''~~Part 9 :~~ Philosophical Implications''' ==		== '''Philosophical Implications''' ==


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	== '''~~Part 10 :~~ Relation to other Research Areas''' ==		== '''Relation to other Research Areas''' ==

	The purpose of this section is to recognize how other popular areas of research are similar to, or are related to the Wolfram Model, in an attempt to bridge the gap and discover how one might apply the Wolfram Model to these other research areas.		The purpose of this section is to recognize how other popular areas of research are similar to, or are related to the Wolfram Model, in an attempt to bridge the gap and discover how one might apply the Wolfram Model to these other research areas.
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	[https://www.youtube.com/watch?v=gM6yb4E9wK0 Nima Arkani Hamed: 1/n (April 17, 2025)]		[https://www.youtube.com/watch?v=gM6yb4E9wK0 Nima Arkani Hamed: 1/n (April 17, 2025)]

			== Notes ==

LukeW at 02:46, 31 July 2025

2025-07-31T02:46:35Z

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	== ~~'''Part 1 : Prerequisites'''~~ ==		== Background ==

	Before diving into the work of Stephen Wolfram, the Wolfram Physics Project, or most projects from the Wolfram Institute, it's helpful to have some background knowledge in certain fields and concepts. If you're unfamiliar with these terms, below are some helpful video links and concise definitions.		Before diving into the work of Stephen Wolfram, the Wolfram Physics Project, or most projects from the Wolfram Institute, it's helpful to have some background knowledge in certain fields and concepts. If you're unfamiliar with these terms, below are some helpful video links and concise definitions.
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	== '''~~Part 2 :~~ New Kind of Science''' ==		== '''A New Kind of Science''' ==
	A New Kind of Science, a book written by Stephan Wolfram in the 1980’s and published in 2002 set the foundations of the Wolfram Model. The book is split into three distinct arcs:		A New Kind of Science, a book written by Stephan Wolfram in the 1980’s and published in 2002 set the foundations of the Wolfram Model. The book is split into three distinct arcs:

	The first arc is a set of experiments where Wolfram [https://en.wikipedia.org/wiki/Proof_by_exhaustion ~~exhaustively]~~ runs classes of rules, making general observations about their behaviour. He observers three key properties about these systems:		The first arc is a set of experiments where Wolfram exhaustively<ref>https://en.wikipedia.org/wiki/Proof_by_exhaustion</ref> runs classes of rules, making general observations about their behaviour. He observers three key properties about these systems:

	# That many simple rules can perform arbitrarily complicated behaviour, specifically behaviour that can not be described by mathematical equations.		# That many simple rules can perform arbitrarily complicated behaviour, specifically behaviour that can not be described by mathematical equations.

Thencourt at 22:54, 13 July 2025

2025-07-13T22:54:40Z

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	Reading a book in less than a few seconds as if it were like a painting on the wall, is like a super power, a term Wolfram often implies when discussing this paradigm. Computationally Irreducible processes contain a lot of power (arguably, the power of the entire universe), because it is the ability to program any system, to compute any computable function:		Reading a book in less than a few seconds as if it were like a painting on the wall, is like a super power, a term Wolfram often implies when discussing this paradigm. Computationally Irreducible processes contain a lot of power (arguably, the power of the entire universe), because it is the ability to program any system, to compute any computable function:

	If we want machine learning to be able to do the best it can, and perhaps give us the impression of “achieving magic”, then we have to allow it to show computational irreducibility.		''"If we want machine learning to be able to do the best it can, and perhaps give us the impression of “achieving magic”, then we have to allow it to show computational irreducibility."''

	Excerpt from : [https://www.youtube.com/watch?v=7BgoJChzb_0 Stephen Wolfram Readings: What’s Really Going On in Machine Learning? Some Minimal Models] - Stephen Wolfram		Excerpt from : [https://www.youtube.com/watch?v=7BgoJChzb_0 Stephen Wolfram Readings: What’s Really Going On in Machine Learning? Some Minimal Models] - Stephen Wolfram

Thencourt at 19:22, 13 July 2025

2025-07-13T19:22:07Z

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	[[File:4 classes of behavior.png\|center\|frame\|100px\|The four classes of behavior that rules typically fall into : homogenous, patterned, random and complex. From Stephan Wolfram, A New Kind of Science]]		[[File:4 classes of behavior.png\|center\|frame\|100px\|The four classes of behavior that rules typically fall into : homogenous, patterned, random and complex. From Stephan Wolfram, A New Kind of Science.]]


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	This animation to the right illustrates these limitations.		This animation to the right illustrates these limitations.

	[[File:Rotating Object.gif\|right\|frame\|500px\|Animation of a rotating object by Clayton Shonkwiler]]		[[File:Rotating Object.gif\|right\|frame\|500px\|Animation of a rotating object by Clayton Shonkwiler.]]

	===Perception===		===Perception===
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	Taking the XY -> XYZ example again, we must force the constraint that XY needed to happen before XYZ happens, since XYZ depends on XY, for an observer that can only see a finite number of these operations occur at a time.		Taking the XY -> XYZ example again, we must force the constraint that XY needed to happen before XYZ happens, since XYZ depends on XY, for an observer that can only see a finite number of these operations occur at a time.

	[[File:Relativity of Simultaneity.gif\|right\|frame\|300px\|]]		[[File:Relativity of Simultaneity.gif\|right\|frame\|300px\|An animation illustrating relativity of simultaneity.]]

	In the large limit, this structure forms the notion of directed time (causality) for an observer: That in order for an event to happen, a previous event must have had already happened. We also start to see how this ambiguity in the structure from an observer's perspective creates the notion of relativity : That if we have two or more of these operations that occur in two different places, say XY -> XYZ over here, and XY - XYZ over there, we have to perceive these in a causal order…where one of those events has to come prior to the other one, and that, depending on where you are embedded in this evolution determines which one happened for them first! ([https://en.wikipedia.org/wiki/Relativity_of_simultaneity Relativity of Simultaneity])		In the large limit, this structure forms the notion of directed time (causality) for an observer: That in order for an event to happen, a previous event must have had already happened. We also start to see how this ambiguity in the structure from an observer's perspective creates the notion of relativity : That if we have two or more of these operations that occur in two different places, say XY -> XYZ over here, and XY - XYZ over there, we have to perceive these in a causal order…where one of those events has to come prior to the other one, and that, depending on where you are embedded in this evolution determines which one happened for them first! ([https://en.wikipedia.org/wiki/Relativity_of_simultaneity Relativity of Simultaneity])

Thencourt at 19:17, 13 July 2025

2025-07-13T19:17:29Z

Thencourt at 19:09, 13 July 2025

2025-07-13T19:09:33Z

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	[[File:CA Shell Transparent.png\|frame\|right\|100px]] An introduction to and conceptually focused walkthrough of the Wolfram Model framework in it’s entirety, serving as a gateway to its materials and resources spread across the internet, for beginners, enthusiasts, and experts alike.		[[File:CA Shell Transparent.png\|frame\|right\|100px\|A seashell found by Hartlabs, that produces a cellular automata pattern.]] An introduction to and conceptually focused walkthrough of the Wolfram Model framework in it’s entirety, serving as a gateway to its materials and resources spread across the internet, for beginners, enthusiasts, and experts alike.

Thencourt at 19:02, 13 July 2025

2025-07-13T19:02:54Z

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	[[File:CA Emulation Map.png\|right\|frame\|100px]]		[[File:CA Emulation Map.png\|right\|frame\|100px]]



	The third and final arc of the book is spent formalizing the observations made in these experiments, by first showing the Elementary Cellular Automata Rule Class emulating each other under different initial conditions. Wolfram and Cook then prove the universality of Rule 110, strongly implying that any rule within this rule class, when given the right initial conditions can lead to an emulation of Rule 110, therefore proving the entire rule class as Turing Universal.		The third and final arc of the book is spent formalizing the observations made in these experiments, by first showing the Elementary Cellular Automata Rule Class emulating each other under different initial conditions. Wolfram and Cook then prove the universality of Rule 110, strongly implying that any rule within this rule class, when given the right initial conditions can lead to an emulation of Rule 110, therefore proving the entire rule class as Turing Universal.

Thencourt at 18:56, 13 July 2025

2025-07-13T18:56:58Z

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			[[File:CA Shell Transparent.png\|frame\|right\|100px]] An introduction to and conceptually focused walkthrough of the Wolfram Model framework in it’s entirety, serving as a gateway to its materials and resources spread across the internet, for beginners, enthusiasts, and experts alike.



	NOTE : WORK IN PROGRESS		NOTE : WORK IN PROGRESS

















	== '''Part 1 : Prerequisites''' ==		== '''Part 1 : Prerequisites''' ==

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	An isomorphism is an equivalence relation between different objects, structures, or systems, proven through a structure-preserving mapping. It ensures that operations, relationships, and transformations in one structure correspond directly to those in another.		An isomorphism is an equivalence relation between different objects, structures, or systems, proven through a structure-preserving mapping. It ensures that operations, relationships, and transformations in one structure correspond directly to those in another.

	[[File:Transformations (small).gif\|right\|frame\|100px]]		[[File:Transformations (small).gif\|right\|frame\|100px\|Depiction of mathematical transformations by Raibatak Das.]]

	=== [https://www.youtube.com/watch?v=YD3HIMUae_4 Transformations] ===		=== [https://www.youtube.com/watch?v=YD3HIMUae_4 Transformations] ===
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	[[File:4 classes of behavior.png\|center\|frame\|100px]]		[[File:4 classes of behavior.png\|center\|frame\|100px\|The four classes of behavior that rules typically fall into : homogenous, patterned, random and complex. From Stephan Wolfram, A New Kind of Science]]


	The second arc of the book is spent making connections between computational rules and how they show up in nature, in system analysis and in fundamental physics.		The second arc of the book is spent making connections between computational rules and how they show up in nature, in system analysis and in fundamental physics.

	[[File:CA Emulation Map.png\|right\|frame\|100px]]		[[File:CA Emulation Map.png\|right\|frame\|100px\|A map of rule emulations of other rules. From Stephan Wolfram A New Kind of Science.]]

	The third and final arc of the book is spent formalizing the observations made in these experiments, by first showing the Elementary Cellular Automata Rule Class emulating each other under different initial conditions. Wolfram and Cook then prove the universality of Rule 110, strongly implying that any rule within this rule class, when given the right initial conditions can lead to an emulation of Rule 110, therefore proving the entire rule class as Turing Universal.		The third and final arc of the book is spent formalizing the observations made in these experiments, by first showing the Elementary Cellular Automata Rule Class emulating each other under different initial conditions. Wolfram and Cook then prove the universality of Rule 110, strongly implying that any rule within this rule class, when given the right initial conditions can lead to an emulation of Rule 110, therefore proving the entire rule class as Turing Universal.
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	The Ruliad is “the entangled limit of all possible rules” and is the most important "true ontology" of the wolfram model. So to conduct faithful science, we study our interface with this object.		The Ruliad is “the entangled limit of all possible rules” and is the most important "true ontology" of the wolfram model. So to conduct faithful science, we study our interface with this object.

	[[File:Ruliad Approximation.png\|right\|frame\|100px]]		[[File:Ruliad Approximation.png\|right\|frame\|100px\|A finite approximation to the Ruliad. From Stephan Wolfram in "The Concept of the Ruliad."]]

	Some properties of the Ruliad are that it is maximally symmetric and countably infinite. From the perspective of the entire object you can think of all mappings as bijective (one-to-one), but for all systems within the Ruliad, all mappings are surjective. In other words, subsystems embedded in this object cannot perceive it without consolidating information about its structure. This will play an important role in observer theory and, subsequently, the Wolfram Model of Physics.		Some properties of the Ruliad are that it is maximally symmetric and countably infinite. From the perspective of the entire object you can think of all mappings as bijective (one-to-one), but for all systems within the Ruliad, all mappings are surjective. In other words, subsystems embedded in this object cannot perceive it without consolidating information about its structure. This will play an important role in observer theory and, subsequently, the Wolfram Model of Physics.
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	This animation to the right illustrates these limitations.		This animation to the right illustrates these limitations.

	[[File:Rotating Object.gif\|right\|frame\|500px\|]]		[[File:Rotating Object.gif\|right\|frame\|500px\|Animation of a rotating object by Clayton Shonkwiler]]

	===Perception===		===Perception===