# Computation and the Fundamental Theory of Physics - with Stephen Wolfram

TLDRThe speaker reflects on the significant changes in the world over the last 45 years, highlighting the rise of computation as a pivotal shift in both technology and intellectual thought. He shares his journey from a young physics enthusiast to a prominent figure in the field, navigating the complex intersection of physics and computation. The discussion delves into the profound progress made in understanding the fundamental theory of physics, facilitated by computational paradigms. The speaker's exploration of cellular automata unveils the surprising complexity that can emerge from simple rules, touching upon the Principle of Computational Equivalence and its broad implications for science and technology. He envisions a future where a computational language could bridge the gap between human thought and the vast potential of the computational universe, allowing us to harness its power to solve complex problems and gain deeper insights into the nature of the universe itself.

###### Takeaways

- π The speaker emphasizes the significant shift in understanding the world through computation, both as a practical tool and as a conceptual framework.
- π The rise of computation has led to substantial progress in understanding complex scientific problems, such as the fundamental theory of physics.
- π§ The speaker's personal journey with computation began with an aversion to complex mathematical calculations, leading to the use of computers as a tool for physics research.
- π The exploration of cellular automata, simple programs that can exhibit complex behavior, has provided insights into the nature of complexity and simplicity in the universe.
- β°οΈ Progress in physics has been facilitated by the integration of computational paradigms with established theories like general relativity and quantum field theory.
- π The use of computer experiments, as opposed to physical ones, allows for the exploration of the computational universe and the discovery of underlying principles of nature.
- π The concept of the Principle of Computational Equivalence suggests that simple programs can perform sophisticated computations, mirroring the complexity observed in natural phenomena.
- π€ The speaker ponders the question of the universe's construction, proposing that it may be governed by a simple underlying program that gives rise to the complexity we observe.
- π The idea that the universe is fundamentally computational has implications for the philosophy of free will, predictability, and the nature of scientific understanding.
- π The computational universe provides a vast space of possibilities that can be mined for models and technological applications, much like natural resources.
- β The development of a computational language that can express and execute thoughts about the world computationally is a major goal, aligning human thought with computational possibilities.

###### Q & A

### What significant change has the speaker identified in the world over the last 45 years?

-The speaker identifies the rise of computation as the most significant change, both as a practical technological aspect and as an intellectual way of thinking about the world.

### What has the speaker been involved in that has contributed to the rise of computation?

-The speaker has been involved in various areas on both the technology and intellectual sides of computation, including particle physics, cosmology, and developing a computational paradigm to understand complex phenomena in nature.

### What is the speaker's view on the progress made in understanding the fundamental theory of physics?

-The speaker is excited about the spectacular progress made in the last year, which was unexpected. The progress was facilitated by leveraging 20th-century physics, including general relativity and quantum field theory, and integrating a computational paradigm.

### How does the speaker describe the use of cellular automata as a tool for understanding complexity in nature?

-The speaker uses cellular automata, simple programs with lines of black and white cells, to demonstrate how very simple rules can lead to complex and sometimes fractal patterns. This suggests that nature could be using simple programs to create complex phenomena.

### What is the significance of rule 30 in the context of the speaker's discussion?

-Rule 30 is significant because it is a simple rule that generates a pattern that appears random and complex. It has been used as a source of pseudorandomness and is an example of how simple computational rules can produce behavior that is computationally irreducible.

### What does the Principle of Computational Equivalence suggest about the relationship between simple rules and sophisticated computations?

-The Principle of Computational Equivalence suggests that once a system's behavior isn't obviously simple, the computations it corresponds to are as sophisticated as any computation that gets done, indicating that simple rules can lead to complex computational outcomes.

### How does the concept of universal computation relate to the idea that simple programs can perform any computation?

-Universal computation is the idea that a single machine can perform any computation given the right initial conditions or program. The Principle of Computational Equivalence supports this by suggesting that any system that isn't doing something obviously simple is capable of universal computation.

### What is the computational universe, and how does it serve as a source of models and technology?

-The computational universe refers to the space of all possible programs and computations. It serves as a source of models for understanding natural phenomena and as a source of technology by providing algorithms and processes that can be mined for various applications.

### How does the speaker's work on computational language aim to bridge the gap between human thought and the computational universe?

-The speaker's work on computational language aims to create a system that allows humans to express thoughts and ideas computationally, which can then be executed by a computer. This bridges the gap by providing a common language that both humans and computers can understand and use to leverage the power of the computational universe.

### What is the speaker's perspective on the possibility of faster-than-light travel in the context of these computational models?

-The speaker views the problem of faster-than-light travel as a generalized engineering problem rather than a physics problem. While it is theoretically possible in the models, it may be practically as impossible as a single gas molecule in a room finding the right path to move faster than light due to computational irreducibility.

### How does the speaker's model of the universe as a network of discrete points, or a hypergraph, challenge traditional assumptions about space?

-The model challenges the traditional assumption that space is continuous and can be divided into infinitesimally small points. Instead, it proposes that space is made of discrete 'atoms of space' that are points in a network, similar to how materials are made of atoms, leading to a discrete and fundamentally different understanding of the fabric of the universe.

###### Outlines

##### π Personal Reflections and the Rise of Computation

The speaker reminisces about their last visit to the Royal Institution in 1975 and reflects on the significant changes in the world since then, highlighting the rise of computation as both a technological and intellectual tool. They discuss their involvement in the development of computational technology and its potential to revolutionize our understanding of fundamental physics. The speaker also shares their early challenges with mathematical calculations in physics and how they began using computers as a tool to overcome these challenges.

##### π The Evolution of Computational Thinking in Physics

The speaker delves into the evolution of their thought process regarding the use of computation in understanding complex phenomena in nature. They discuss the limitations of traditional mathematical physics methods and the shift towards using computational models, such as cellular automata, to simulate natural processes. The speaker presents a computer experiment with cellular automata to illustrate how simple rules can lead to complex and sometimes fractal patterns, hinting at the underlying simplicity of nature's complexity.

##### π€ Exploring the Computational Universe and its Potential

The speaker explores the concept of a computational universe filled with possible programs and the idea that simple rules can produce incredibly complex behavior. They discuss the Principle of Computational Equivalence, which suggests that once a system's behavior surpasses simplicity, its computation is as sophisticated as any other. This principle has profound implications for understanding the nature of computation, the predictability of systems, and the development of technology and modeling in science.

##### π§ The Computational Language and its Impact on Science and Technology

The speaker discusses the creation of a computational language that allows for the expression of ideas in a way that is understandable by both humans and computers. They highlight the importance of integrating world knowledge into this language, enabling the translation of natural language into precise computational instructions. The speaker also touches on the historical shift from mathematical equations to programming for modeling in science and the technological applications of the computational universe.

##### π Ambitious Computational Models and the Fundamental Theory of Physics

The speaker shares their ambitious idea of using simple computational programs to describe the universe, which led to significant progress in understanding the fundamental theory of physics. They discuss the concept that the universe might be made up of discrete points in a network, challenging the continuous nature of space. The speaker also talks about the influence of 20th-century physics and the integration of computational paradigms into our understanding of the universe.

##### β¨ The Structure of Space and the Progression of Time

The speaker describes their model of space as a network or hypergraph of discrete points, where the connections between points represent the fabric of space. They argue that space is not continuous and that its large-scale continuity is an emergent property. The speaker also redefines the concept of time as a process of computation, where the continuous rewriting of the hypergraph represents the progression of time, leading to a model that aligns with Einstein's theory of special relativity.

##### βοΈ Energy, Matter, and the Unification of Physics Theories

The speaker explores how the hypergraph model can account for the concepts of energy and matter, and how these concepts lead to the full version of Einstein's equations. They discuss the idea that energy is a measure of activity within the network and that this activity can be related to the energy density in the model. The speaker also touches on the concept of geodesics in the context of general relativity and how these concepts apply within their hypergraph model, including the formation of black holes and the possibility of faster-than-light travel.

##### π The Multi-Way Graph and the Nature of Quantum Mechanics

The speaker introduces the concept of a multi-way graph that inherently includes the principles of quantum mechanics, where multiple possible updates to the system lead to a branching of paths, analogous to the multiple possible outcomes in quantum systems. They explain how this naturally incorporates the uncertainty and probabilistic nature of quantum mechanics, and how the Feynman Path Integral can be derived from the properties of these graphs, providing a new perspective on the complex numbers and amplitudes in quantum theory.

##### π The Interplay Between Physics and Computation

The speaker discusses the parallels between the deflection of geodesics in physical space due to energy (leading to Einstein's equations) and the same phenomenon in 'bronchial space' (leading to the Feynman path integral), suggesting that general relativity and quantum field theory are essentially different expressions of the same underlying theory. They also touch on the implications of their models for understanding black holes and the potential for dimension changes in the early universe.

##### π The Search for a Fundamental Rule of Physics

The speaker ponders the implications of discovering a simple, fundamental rule that describes the entire universe, questioning why we should be so fortunate as to have a universe that is fundamentally simple. They introduce the concept of a 'rulial multi-way graph' that allows for different rules to be applied at each step, and discuss how this framework leads to the idea that finding a fundamental theory of physics is akin to designing a computational language that can describe the universe in a way that is useful to us.

##### π¬ The Convergence of Mathematics and Physics

The speaker concludes by emphasizing the computational view of the universe and how it has influenced the last 45 years of scientific thought. They express excitement about the potential for a fundamental understanding of physics through computation and the possibility of a 'machine code' underlying all known physics. The speaker also suggests that abstract mathematical concepts may converge with physics, and that the search for a fundamental theory of physics is a language design project, with the goal of finding a description language that represents the universe in a way that is coherent and useful.

###### Mindmap

###### Keywords

##### π‘Computation

##### π‘Cellular Automata

##### π‘Fundamental Theory of Physics

##### π‘Quantum Field Theory

##### π‘General Theory of Relativity

##### π‘Computational Universe

##### π‘Principle of Computational Equivalence

##### π‘Universal Computation

##### π‘Causal Graph

##### π‘Effective Dimension

##### π‘Curvature

###### Highlights

The speaker reflects on the significant rise of computation as both a practical technology and an intellectual framework for understanding the world over the last 45 years.

Recent advancements have been described as 'spectacular progress' in the pursuit of understanding the fundamental theory of physics.

The integration of computation with established physics theories like general relativity and quantum field theory has opened new avenues in scientific understanding.

The speaker's early interest in physics and overcoming the barrier of complex mathematical calculations led to the use of computers as a tool for physics.

Cellular automata are introduced as simple programs that can exhibit surprisingly complex behavior, hinting at the underlying simplicity of natural phenomena.

Rule 30 cellular automaton is highlighted for its ability to generate patterns that appear random, yet are determined by a simple rule, influencing cryptography and language.

The Principle of Computational Equivalence suggests that simple programs can perform as sophisticated computations as any other, challenging traditional engineering intuitions.

The concept of universal computation is discussed, emphasizing the impact of a single machine running different programs for varied computational tasks.

The computational universe is portrayed as a rich source of models for natural phenomena and a potential gold mine for new technological applications.

The speaker's work on creating a computational language to bridge human thoughts with the execution of computational tasks is outlined.

The idea that the universe might be fundamentally constructed by a simple program leading to emergent complexity is explored.

Space is proposed to be discrete, made of points connected in a hypergraph network, contrary to traditional continuous space assumptions.

Time is considered as a process of computation where the continuous rewriting of the hypergraph network represents its progression.

The large-scale behavior of the spatial hypergraph network is shown to align with Einstein's general theory of relativity, offering a new perspective on space and gravity.

Quantum mechanics emerges inevitably from the multi-way system of updates in the hypergraph, suggesting a deep connection between computation and quantum phenomena.

The speaker posits that finding the fundamental theory of physics is akin to a language design project, aiming to find a description language for the universe that is useful to us.

The potential existence of multiple, incoherent description languages for the universe is discussed, suggesting that our understanding of physics is tied to our human perspective and experience.

The convergence of abstract mathematical ideas, such as higher category theory, with physics is highlighted as a remarkable outcome of the computational approach to physics.

###### Transcripts

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