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Stephen Wolfram is the creator of Mathematica and Wolfram|Alpha and the author of A New Kind of Science and An Elementary Introduction to the Wolfram Language. In this short ebook, Dr. Wolfram dives into his theories of computation and the universe.
Take a look at this short excerpt from the ebook Computation and the Future of the Human Condition:
“In traditional engineering, one starts with some purpose in mind, then explicitly tries to construct a system that achieves that purpose.
And typically at each step one insists on foreseeing what the system will do.
With the result that the system must always be quite computationally reducible.
But in the computational universe there are lots of systems that aren’t computationally reducible.
So can we use these systems for technology?
The answer is absolutely yes.
Sometimes we look at the systems and realize that there’s some purpose for which they can be used.
But more often, we first identify a purpose, and then start searching the computational universe for systems that can achieve that purpose.
Things like this have been done a little in traditional engineering—even, say, with
Edison searching for his light-bulb filaments.
But it’s vastly more efficient and streamlined in the computational universe.
John von Neumann
Finally We May Have a Path to the Fundamental Theory of Physics... and It's Beautiful
I Never Expected This · How It Works · All Possible Rules · What Is Space? · The Dimensionality of Space · Curvature in Space & Einstein's Equations · Time · The Graph of Causal Relationships · The Importance of Causal Invariance · Deriving Special Relativity · What Is Energy? What Is Mass? · General Relativity and Gravity · Black Holes, Singularities, etc. · Cosmology · Elementary Particles--Old and New · The Inevitability of Quantum Mechanics · General Relativity and Quantum Mechanics Are the Same Idea! · Branchial Motion and the Entanglement Horizon · Finding the Ultimate Rule · Why This Universe? The Relativity of Rules · The Challenge of Language Design for the Universe · Let's Go Find the Fundamental Theory!
A Class of Models with the Potential to Represent Fundamental Physics
Introduction · Basic Form of Models · Typical Behaviors · Limiting Behavior and Emergent Geometry · The Updating Process for String Substitution Systems · The Updating Process in Our Models · Equivalence and Computation in Our Models · Potential Relation to Physics · Notes & Further References
How We Got Here: The Backstory of the Wolfram Physics Project
"Someday..." · Why Wasn't This Already Figured Out? · The Beginning of the Story · "You Can't Leave Physics" · Maybe It Could Apply to Physics · "Please Don't Do That Project" · Two Young Physicists and a Little Idea · Oh My Gosh, It's Actually Going to Work! · What Terrible Timing! · What Happens Now
A New Kind of Science: a 15-Year View (2017)
What Is Spacetime, Really? (2015)
Fundamental Physics, from A New Kind of Science (2002)
Historical & Technical Notes
In a world where jobs are continually being outsourced to machines and algorithms, the question of how best to educate the next generation becomes more important with every year. Stephen Wolfram, author of A New Kind of Science and Idea Makers and creator of Wolfram|Alpha, says the answer is computational thinking. Wolfram defines computational thinking as "formulating things with enough clarity that one can tell a computer how to do them." Computational thinking provides the most direct link possible between idea and implementation, without the repetitiveness and minutia of basic programming languages. Wolfram walks the reader through the basics of the Wolfram Language, encouraging young minds to embrace these concepts, while allowing them to creatively explore beautiful visualizations and actual working code. The Wolfram Language is free for anyone with a web browser to experiment with and use.
Wolfram discusses the history of computation from its earliest beginnings to current applications and the emergence of computable knowledge. Notable figures include: Pythagoras, Archimedes, Isaac Newton, Galileo, Gottfried Leibniz, Carl Linnaeus, John von Neumann, and many others.
Combinators: A Centennial View:
Ultimate Symbolic Abstraction • Computing with Combinators • A Hundred Years Later... • Combinators in the Wild: Some Zoology • Visualizing Combinators • Updating Schemes and Multiway Systems • The Question of Evaluation Order • The World of the S Combinator • Causal Graphs and the Physicalization of Combinators • Combinator Expressions as Dynamical Systems • Equality and Theorem Proving for Combinators • Lemmas and the Structure of Combinator Space • Empirical Computation Theory with Combinators • The Future of Combinators • Historical & Other Notes
Combinators and the Story of Computation:
The Abstract Representation of Things • What Is Mathematics―and Logic―Made Of? • Combinators Arrive • What Is Their Mathematics? • Gödel's Theorem and Computability • Lambda Calculus • Practical Computation • Combinators in Culture • Designing Symbolic Language • Combinators in the Computational Universe • Combinators All the Way Down?
Where Did Combinators Come From? Hunting the Story of Moses Schönﬁnkel:
December 7, 1920 • Who Was Moses Schönﬁnkel? • The Beginning of the Story • Going to College in Odessa • Göttingen, Center of the Mathematical Universe • Problems Are Brewing • The 1924 Paper • The "1927" Paper • To Moscow and Beyond... • Other Schönﬁnkels... • Haskell Curry • Schönﬁnkel Rediscovered • What Should We Make of Schönﬁnkel?
A Little Closer to Finding What Became of Moses Schönfinkel, Inventor of Combinators
1920, 2020 and a $20,000 Prize: Announcing the S Combinator Challenge:
Hiding in Plain Sight for a Century? • The Basic Setup • The Operation of the S Combinator Challenge
Excerpts from A New Kind of Science (2002)
A Bibliography of Combinators:
Foundational Documents • Books • Surveys & Summaries • Combinators as Symbolic Expressions • Combinators as Mathematical Constructs • Combinator Computation • Extensions & Applications • Confusing Issues