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Charting a Course for Complexity : Metamodeling, Ruliology and More—Stephen Wolfram Writings
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science—Stephen Wolfram Writings
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How Inevitable Is the Concept of Numbers?
May 25, 2021
Everyone Has to Have Numbers… Don’t They?
The aliens arrive in a starship. Surely, one might think, to have all that technology they must have the idea of numbers. Or maybe one finds an uncontacted tribe deep in the jungle. Surely they too must have the idea of numbers. To us numbers seem so natural and “obvious” that it’s hard to imagine everyone wouldn’t have them. But if one digs a little deeper, it’s not so clear.
It’s said that there are human languages that have words for “one”, “a pair” and “many”, but no words for specific larger numbers. In our modern technological world that seems unthinkable. But imagine you’re out in the jungle, with your dogs. Each dog has particular characteristics, and most likely a particular name. Why should you ever think about them collectively, as all “just dogs”, amenable to being counted?
January 21, 2021
It All Started with Feynman Diagrams
Any serious calculation in particle physics takes a lot of algebra. Maybe it doesn’t need to. But with the methods based on Feynman diagrams that we know so far, it does. And in fact it was these kinds of calculations that first led me to use computers for symbolic computation. That was in 1976, which by now is a long time ago. But actually the idea of doing Feynman diagram calculations by computer is even older.
So far as I know it all started from a single conversation on the terrace outside the cafeteria of the CERN particle physics lab near Geneva in 1962. Three physicists were involved. And out of that conversation there emerged three early systems for doing algebraic computation. One was written in Fortran. One was written in LISP. And one was written in assembly language.
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