
Here are my notes from Wolfram’s talk. He pulled up a visualization of the first 400 rows of Rule 30 (see comments below) in his exploration of the simple iterative math of cellular automata:
“Rule 30 is my favorite discovery in all of science. I first saw in 1982. I didn’t appreciate it at first. It is like turning a telescope into the mathematical universe and seeing the moons of Jupiter for the first time.”
“Rule 30 was the random number generator for Wolfram Alpha for many years. We screened trillions of alternatives before finding more efficient one.”
Wolfram mentioned Estonia ten times in his query examples. Such a warm start.
“I started to study cellular automata in 1980. I wanted to study neural networks but they were too much of a mess. So I went to cellular automata.”
“I have become interested in smart contracts. Proof of work in Ethereum is an instance of computational irreducibility.”
In response to my question at the end: “We are stuck in a universe that is stuck with the computational constraints of a Turing machine. That is why we have computational irreducibility. But the frontier of interesting theorems expands forever. We will never invent all of the interesting things.”
“Evolution is a lame way of explaining what’s possible. It only explores small moves.”
In 2004, I asked Wolfram about quantum computational equivalence.
I still wonder if quantum computers will overturn the constraints of the Turing thesis. See Aaronson’s comments here
Speaking at the Age of AI today

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