Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist. This is our second conversation on the podcast. Please check out our sponsors to get a discount and to support this podcast: - SimpliSafe: https://simplisafe.com/lex - Sun Basket, use code LEX: https://sunbasket.com/lex - MasterClass: https://masterclass.com/lex If you would like to get more information about this podcast go to https://lexfridman.com/podcast or connect with @lexfridman on Twitter, LinkedIn, Facebook, Medium, or YouTube where you can watch the video versions of these conversations. If you enjoy the podcast, please rate it 5 stars on Apple Podcasts, follow on Spotify, or support it on Patreon. Here's the outline of the episode. On some podcast players you should be able to click the timestamp to jump to that time. OUTLINE: 00:00 - Introduction 07:14 - Key moments in history of physics 12:43 - Philosophy of science 14:37 - Science and computational reducibility 22:08 - Predicting the pandemic 38:58 - Sunburn moment with Wolfram Alpha 39:46 - Computational irreducibility 46:45 - Theory of everything 52:41 - General relativity 1:01:16 - Quantum mechanics 1:06:46 - Unifying the laws of physics 1:12:01 - Wolfram Physics Project 1:29:53 - Emergence of time 1:34:11 - Causal invariance 1:53:03 - Deriving physics from simple rules on hypergraphs 2:07:24 - Einstein equations 2:13:04 - Simulating the physics of the universe 2:17:28 - Hardware specs of the simulation 2:24:37 - Quantum mechanics in Wolfram physics model 2:42:46 - Double-slit experiment 2:45:13 - Quantum computers 2:53:21 - Getting started with Wolfram physics project 3:14:46 - The rules that created our universe 3:24:22 - Alien intelligences 3:32:29 - Meta-mathematics 3:37:58 - Why is math hard? 3:52:55 - Sabine Hossenfelder and how beauty leads physics astray 4:01:07 - Eric Weinstein and Geometric Unity 4:06:17 - Travel faster than speed of light 4:16:59 - Why does the universe exist at all
The conversation highlights the potential of using simple rules that work on hypergraphs and cellular automata to generate the infrastructure from which space, time, and modern physics emerge which can be significant for innovative research in math, computer science, and physics. The dialogue showcases the importance of hypergraphs and cellular automata in developing fundamental ideas about intelligence, consciousness, and the fundamental laws of physics.
The low-hanging fruit in fundamental physics has been rapidly picked and there is still a long way to go, however, there is a significant phenomenon that allows simple programs to create complex structures.
The concept of computational irreducibility means that even if you understand the rules by which something operates, you may not be able to predict what it will do. This limitation exists in science, and while it has received significant attention, it is more of a conceptual inspiration than a practical tool in research.
The concept of human narratives is flawed because it constructs things that are not representative of reality. While people want a clear explanation of events like the pandemic, there is no grand story arc that explains the complexity of the situation.
The complexity of human interactions and computational processes can lead to a lack of understanding in fields like science and society, where predictions are based on limited knowledge of the system. The story of thermodynamics serves as an analogy to this concept of computational irreducibility.
The idea that science can provide us with all the answers to problems is impractical as it could potentially rob us of experiences that shape our lives. Computational irreducibility means there are some things in life that science won't always be able to solve, hence politicians have the responsibility of making important decisions.
The guest explains how computations in nature are essential for understanding the world around us and making predictions possible.
The search for a complete, formal theory of physics that could reproduce any physical phenomena is hindered by computational irreducibility. Despite this, scientists continue to search for a fundamental theory that could relate general relativity to quantum mechanics.
The evolution of physics can be traced back from ancient Greek philosophy to modern-day cosmology. The approach to physics has shifted to using mathematical principles and equations to explain natural phenomena such as the behavior of light.
The transcript explains the development of quantum mechanics, which is a theory of wave functions used to calculate various features of the microscopic world. It also mentions its successful application in the standard model of particle physics, helping to understand how atoms work.
Abstract concepts in mathematics, such as higher category theory and infinity groupoids, have proven to be relevant in describing how our universe works, particularly in the context of black holes and the combination of quantum effects with general relativity. Despite their complexity, these concepts are essential in understanding physics and building structures to explain the universe.
The concept of space as a discrete entity with "atoms" of space is explored in this podcast. This idea leads to mathematical models that can describe large scale space interactions that mimic the properties of continuous space on a smaller scale.
In this podcast episode, the host delves into the concept of hypergraphs - specifically, the hypergraph of space. The discussion revolves around the elements that make up the structure of space and how they are represented in the hypergraph.
The application of a rule in the fundamental theory of physics can be thought of as an event that transforms a piece of hypergraph into another piece of hypergraph, and requires the existence of the previous atom of space for another transformation to occur. The rule may look simple on paper, but the application of it can be complex.
Exploring the mathematical formalism behind unifying space and time, as the rules of special relativity suggest that space and time are fundamentally the same.
The causal graph represents the unique graph of causal relationships between events, meaning that if an event depends on the output of another event, there will be a causal relationship between them. This implies that the graph of causal relationships is invariant regardless of the perspective or viewpoint.
The points in a graph that are neighbors can be projected in two dimensions to approximate a two-dimensional structure. By using the causal relationships between connected updates, a basic structure for updating the graph can be established.
In this episode, the concept of the curvature of space is explored and how it affects measurements of area on a sphere. Additionally, the discussion delves into properties of the universe and the excitement surrounding the discovery of rules that correspond to what is already known.
Our universe may not be strictly three dimensional, as there may be areas that are 3.01 or 2.99 dimensional. However, as long as there is causal invariance and computational irreducibility, and the space is non-infinite dimensional, it can still exist.
The combination of numerical relativity and parallel programming is giving us new ways to think about all possible things happening in parallel, as scientists take the mathematical equations, break them down, and run them on a computer to analyze and understand the universe better.
Time is a constant factor in all variations of how we think about the universe, as it is computation itself. Elementary time is the amount of time that elapses through a single computational step.
The maximum entanglement speed is like a maximum speed in the space of quantum states, just as the speed of light is a maximum speed in physical space, and it can be measured in black hole systems. The concept of fermions versus bosons plays a fundamental role in the exclusion principle that prevents matter from self-destructing.
This podcast explains the concept of the theory of quantum measurement and how it relates to multiway graphs where there are several possible choices at each node, leading to different outcomes.
This episode explores the concept of branchial space, which is the space of quantum states that describes the relationships between things, not in physical space, but in the space of quantum states.
The underlying equation for the motion in branchial and physical space is the same. The Feynman path integral formulation allows interpreting quantum mechanics in terms of mathematics that can be explained in ordinary space.
The measurement process in quantum mechanics may limit the possible advantages of quantum computing for computation. The use of brontial space may provide a way to utilize the expansion of the universe for quantum computing.
The application of the rule in a hypergraph helps in building the true story of how the double-slit experiment works. Even beginners can explore it and contribute strong ideas that are publishable.
The latest episode of the Wolfram Physics Project features Stephen Wolfram discussing the work of the project from a non-physicist's point of view and explaining how it can be accessible to anyone interested in computation and formal abstract ideas.
The exclusion principle in branchal space results in particles with half integer spin called fermions, such as electrons, tending to stay apart while bosons, like photons, have integer spin and love to get together in the same state, leading to phenomena like lasers.
The speaker discusses their journey through physics and how they are now returning to apply their knowledge in the field.
By looking at the extreme non-deterministic Turing machines, we are mapping out all the possible paths with an infinite number of branches that the machine can follow. These multiway graphs represent the space of all possible branching possibilities of a non-deterministic Turing machine.
The fundamental principle of our universe is that it is computational and different interpretations of physics correspond to running physics on different underlying rules like different computers. This has implications for how we think about intelligence and the nature of the universe.
There are maximum speeds of information transmission in physical space, brachial space (entanglement), and ruellial space (translation between different description languages). There may be a connection between physical energy and computation theory.
Stephen Wolfram discusses the parallels between observers in physics and the axiom systems of mathematics, along with the concept of category theory as an idealized theory of mathematics.
The use of automated theorem proving in physics helps in understanding multiway graphs, and its occurrence in the field of cellular automata serves as a minimal model for road traffic flow.
The speaker discusses the work of a researcher who obtained a PhD in mathematical physics from Harvard, noting that they are working to come up with a fundamental theory of physics, and comments on the challenges of working in a mature field.
The possibility of the local gauge invariance in particle physics being generic and tied to various abstruse areas of mathematical physics is explored, offering exciting prospects for the fundamental theory of physics.
The concept of computational irreducibility in physics limits certain aspects of science; however, it serves as a grounding for other scientific theories and has vast implications for the philosophy of how we think about things.
The speaker discusses their fascination with people and the human experience, as well as their interest in figuring out new ideas and testing the limits of their imagination.
The speaker reflects on the importance of human existence in physics and how we are significant simply because we exist. It is a funny feeling to realize that our role is not to make something amazing but to just be content with the fact that we are here.