Wednesday, May 27, 2020

Different Than Penrose and Weinstein: Wolfram REALLY Mesmerized By Rule 30

dr.brian.keating |  On the philosophical front, we compared Godel to Popper and discussed computational irreducibly which arose from Stephen’s interest in Godel and Alan Turing’s work.

“Actually, there’s even more than that. If the microscopic updatings of the underlying network end up being random enough, then it turns out that if the network succeeds in corresponding in the limit to a finite dimensional space, then this space must satisfy Einstein’s Equations of General Relativity. It’s again a little like what happens with fluids. If the microscopic interactions between molecules are random enough, but satisfy number and momentum conservation, then it follows that the overall continuum fluid must satisfy the standard Navier–Stokes equations. But now we’re deriving something like that for the universe: we’re saying that these networks with almost nothing “built in” somehow generate behavior that corresponds to gravitation in physics. This is all spelled out in the NEW KIND OF SCIENCE book. And many physicists have certainly read that part of the book. But somehow every time I actually describe this (as I did a few days ago), there’s a certain amazement. Special and General Relativity are things that physicists normally assume are built into theories right from the beginning, almost as axioms (or at least, in the case of string theory, as consistency conditions). The idea that they could emerge from something more fundamental is pretty alien. The alien feeling doesn’t stop there. Another thing that seems alien is the idea that our whole universe and its complete history could be generated just by starting with some particular small network, then applying definite rules. For the past 75+ years, quantum mechanics has been the pride of physics, and it seems to suggest that this kind of deterministic thinking just can’t be correct. It’s a slightly long story (often still misunderstood by physicists), but between the arbitrariness of updating orders that produce a given causal network, and the fact that in a network one doesn’t just have something like local 3D space, it looks as if one automatically starts to get a lot of the core phenomena of quantum mechanics — even from what’s in effect a deterministic underlying model. OK, but what is the rule for our universe? I don’t know yet. Searching for it isn’t easy. One tries a sequence of different possibilities. Then one runs each one. Then the question is: has one found our universe?”
My question: that was then, what do you think now?
On the implications of finding a simple rule that matches existing laws of physics:
I certainly think it’ll be an interesting — almost metaphysical — moment if we finally have a simple rule which we can tell is our universe. And we’ll be able to know that our particular universe is number such-and-such in the enumeration of all possible universes. It’s a sort of Copernican moment: we’ll get to know just how special or not our universe is. Something I wonder is just how to think about whatever the answer turns out to be. It somehow reminds me of situations from earlier in the history of science. Newton figured out about motion of the planets, but couldn’t imagine anything but a supernatural being first setting them in motion. Darwin figured out about biological evolution, but couldn’t imagine how the first living cell came to be. We may have the rule for the universe, but it’s something quite different to understand why it’s that rule and not another. Universe hunting is a very technology-intensive business. Over the years, I’ve gradually been building up the technology I think is needed — and quite a bit of it is showing up in strange corners of Mathematica. But I think it’s going to be a while longer before there are more results. And before we can put “Our Universe” as a Demonstration in the Wolfram Demonstrations Project. And before we can take our new ParticleData computable data collection and derive every number in it. But universe hunting is a good hobby.”

It’s awfully easy to fall into implicitly assuming a lot of human context. Pioneer 10 — the human artifact that’s gone further into interstellar space than any other (currently about 11 billion miles, which is about 0.05% of the distance to α Centauri) — provides one of my favorite examples. There’s a plaque on that spacecraft that includes a representation of the wavelength of the 21-centimeter spectral line of hydrogen. Now the most obvious way to represent that would probably just be a line 21 cm long. But back in 1972 Carl Sagan and others decided to do something “more scientific”, and instead made a schematic diagram of the quantum mechanical process leading to the spectral line. The problem is that this diagram relies on conventions from human textbooks — like using arrows to represent quantum spins — that really have nothing to do with the underlying concepts and are incredibly specific to the details of how science happened to develop for us humans.”

From the audience he responded to some questions including “what does he believe a scientific theory should be?” and “Does mathematical beauty matter at all, or is it just falsifiability?”
The Story of Rule 30
How can something that simple produce something that complex? It’s been nearly 40 years since I first saw rule 30 — but it still amazes me. Long ago it became my personal all-time favorite science discovery, and over the years it’s changed my whole worldview and led me to all sorts of science, technology, philosophy and more.