A conversation between Gregory Chaitin and Stephen Wolfram at the Wolfram Summer School 2021 

Two legends discussing philosophy of math - thank you for posting these conversations!

29:00 This's Brouwer's conception of the whole of mathematics lol

What Chaitin was referring to at 1:22:42 is called the Extended Evolutionary Synthesis (ESS) and includes such things as epigenetics (which he mentions) niche construction, stress directed mutations, genome duplications, transposon insertions, and mechanisms for genomic re engineering by the organism, as well as convergence and evo devo. All of these are confirmatory of Chaitin's point that simple mutations like SNPs and Indels are insufficient to explain evolutionary change. However, Wolfram is correct and Chaitin is wrong about any correlation between genome size and biological complexity. This is where gene expression, rather than gene sequence comes in, as mentioned earlier by Wolfram. It is very heartwarming to see such brilliant physicists trying to learn, understand, and calculate biology. Keep at it guys. We biologists need all the help we can get.

Great interview. Hopefully He'll be back, more on the omega number!

Interesting that Chaitin was skeptical about Gödel's incompleteness theorems. I recently looked at the Peano axioms and they lack an axiom for total order! I wonder if Gödel's theorems work because of only partial order.

1:25:00 What is the looping code that doesn't halt called? 1:26:26 Stephan mentions a primitive recursive function with 6 symbols, what is it called?

From minute 50 to 53 - @Stephen Wolfram - The uniting of mathematics and art makes possible the universe of all possible programs. I would love to talk to you about this.

Because of computational irreducibility we will never find an algorithm describing Steven Wolfram. However there is most likely a cellular automaton in the computational universe that could be Steven Wolfram. Is this correct? Is a cellular automaton an algorithm or just an automaton? I read that cellular automaton are probably not reversible.

(Name misspelled?)

What is that paper by E. F. Moore?

I use metabiology during a discussion on quantum genetics on Medium. The "platonic" math for evolution discussed is going to be hyperbolic statistics of negative chemical concentration ancestry not full on program size complexities in surreal number representations.

I probably going to state the obvious here although the group of Turing equivalent machines produce same results, that does not mean they have same computational complexity producing the result.. So how do we know if we found and use an efficient one, "well that of course computation time doing tasks", but more in general if it is an efficient "way" to do computations? Stephen do you think that computers are Turing machines of high efficiency or could there be totally different "ideas?/architectures?" that turns out to be vastly superior? I guess to prove that one would have to prove that we do math arithmetic and calculus, algebra, trigonometry and geometry effective?

@53:00 there is no way I'd let anyone get away with, "The universe is all possible programs." If you learn nothing else from Gödel you should learn some things _could_ exist which are not computable, not programs, not even describable in any formal language even admitting an infinite alphabet. I'd even argue non-computable non-algorithmic non-programmable unknowable realities _must_ exist, or if not "must exist," then in some probabilistic sense "almost surely exist with vanishing probability of not existing." (in any platonic sense you care to envisage for defining the concept "reality"). I'd say provably to that too (I do not have the proof to hand, I left it in the margins of the html code for this page.) The mathematics of even the simplest number theory requires this I suspect, unless you are prepared to accept the limitations of finitism (and why would you?, finitism is a vulgar (or banal?) convenience, and nothing more, suitable for computer scientists who do not want to handle symbols involving or implicating transfinite numbers) or as Gödel might have said, "a prejudice of our times."

1:11:58 Leigh Van Valen

The Fecund Universe hypothesis implies endless creativity to the Universal computations! This lines up with the implications of Gödel's theorems! "There is always more for Life to do!"

two of the smartest people alive! 5k views. the world sucks.

Gregory John Chaitin

Male intrasexual selection following on predation reduced panmixia which would permit greater rates of speciation over the same ecological range: That may explain the Cambrian Explosion's apparent coincidence with shells.

Why are we trying to "precompute" anything? Allow many computations to occur in a scheme that has opportunistic confluence and synchrony and look at the patterns of Bisimilarity and ecologies that emerge.

@54:00 that is complete ahistorical nonsense from Stephen. The Platonic solids came from pure geometry, not a physics study of crystals. Don't give science a bad name by trying to re-write history they way you fantasise it to be making the Greeks out to be geniuses they were not.

What a terrible video....really really bad you missed every opportunity to talk about his ideas and talked about frivolous rubbish.

@1:14:00 that was mystical nonsense. Black holes are not an "end of time," they evaporate (afawk). Learn some real physics Mr Wolfram.