The majority problem, or density classification task, is the problem of finding one-dimensional cellular automaton rules that accurately perform majority voting. Using local transition rules, cells cannot know the total count of all the ones in system. In order to count the number of ones (or, by symmetry, the number of zeros), the system requires a logarithmic number of bits in the total size of the system. It also requires the system send messages over a distance linear in the size of the system and for the system to recognize a non-regular language. Thus, this problem is an important test case in measuring the computational power of cellular automaton systems. (Wikipedia).
Turing Machines and The Halting Problem (Part 2)
The Halting Problem has fascinated thousands of computer scientists from around the world. A major part of Computing Logic, the proof of the halting problem proves that computers can't do everything. Check out the video to learn more about why computers work the way they do! For Turing Ma
From playlist Math
C49 Example problem solving a system of linear DEs Part 1
Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.
From playlist Differential Equations
Democracy is mathematically impossible.
Determining the "will of majority" is badly defined. Why should we believe the two- round voting system if there are many other ways to quantify people's preferences ? In this video I discuss the manipulations, paradoxes and other problems associated with the mathematics of voting. My
From playlist Something you did not know...
Solve a System of Equations Using Elimination with Fractions
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Wolfram Student Podcast Episode 6: Computationally Generated Music Based on Lyrics
In our 6th episode of the Wolfram Student Podcast, we talk to Sohum Bajaj about his project on computationally generating music based on lyrics. Join us as we discuss how to computationally represent pitch and sentiment, and cellular automata’s role in music! If you would like to be feat
From playlist Wolfram Student Podcast
C20 Example problem using the superposition principle
Another example problem.
From playlist Differential Equations
B06 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
Laurent Bartholdi: Amenable groups - Lecture 2
Abstract: I shall discuss old and new results on amenability of groups, and more generally G-sets. This notion traces back to von Neumann in his study of the Hausdorff-Banach-Tarski paradox, and grew into one of the fundamental properties a group may / may not have -- each time with import
From playlist Mathematical Aspects of Computer Science
Cellular automata: emergence in not-so-complex systems
In this video we explore the concept of emergence through the lens of cellular automata. 00:00 Intro 02:13 Our model system, the cellular automaton 04:56 Visualizing automata through time 05:12 Types of automata, from periodicity to chaos 08:24 Looking for emergence in cellular automata
From playlist Summer of Math Exposition Youtube Videos
What We've Learned from NKS Chapter 11: The Notion of Computation
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
What We've Learned from NKS Chapter 10: Processes of Perception and Analysis
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
The Curtis-Hedlund-Lyndon Theorem | Nathan Dalaklis | math academic talks
This is the second seminar talk that I have given as a math phd student. It is an expository academic talk that I gave as a Math PhD student during my second semester of my second year in my PhD program. The talk concerns the Factors of Symbolic Dynamical Systems and is focused on the Curt
From playlist Academic Talks
Using Two Multipliers to Solve a System of Equations with Elimination
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
What We've Learned from NKS Chapter 6: Starting from Randomness
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Using Multipliers to Solve a System of Equations Using Elimination
đŸ‘‰Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Hard
Stephen Wolfram's Picks of Cellular Automata from the Computational Universe
Join our inaugural liveminting event, where you'll see the live creation of unique NFTs for Stephen Wolfram's picks of cellular automata from the computational universe. Mint your own NFT in the Wolfram Language using the Wolfram Function Repository function MintNFT: https://resources.wol
From playlist Stephen Wolfram Livestreams