The Ruliology of Lambdas
Posted4 months agoActive3 months ago
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Stephen Wolfram's post explores the 'ruliology of lambdas', delving into lambda calculus and its visualizations, sparking discussion on the value and insight gained from such explorations.
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Sep 15, 2025 at 3:28 PM EDT
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Sep 19, 2025 at 6:02 AM EDT
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The post would have benefited from explaining what will be found clearly in an initial paragraph, instead of endlessly meandering. As it is now, it feels like wanting to find anything spectacular, but actually finding nothing. Well, except for made up term "ruliology" that is not defined.
If you found the visualizations pointless, then you aren't the intended audience. This is a straightforward continuation of his existing research into computation, which started with cellular automata. If you're reading a Wolfram blog, then you're in part coming for the pretty pictures.
> The probably invented term "ruliology" is not even explained anywhere.
The "ruliad" is what he calls the "space of all possible rules" where a rule is like a program that dictates the next state of the system. The ruliad is one of the few rigorous approaches to answering why the laws of physics are the way they are. Stephen's theory is something like "every possible rule for evolving the system is in fact happening, and we are likely to be observing phenomenon that are convergent among more than one rule".
His physics project is a good example of what real physics looks like outside of academia. Stephen is financially independent. He can research whatever he wants and doesn't have to worry about tenure, or sucking up to department heads or people with grant money. Even so, he's not a crank, other physicists understand and engage with what he's doing, and all the math involved is very real.
Just to pour some more opinions on the fire, I think he's been descending into crankery slowly, but steadily, since the 80s. Have a sconce at what his output was like before he took m-expressions and built a paywall around them, become a fairly wealthy demigod of science in the process. https://www.stephenwolfram.com/publications/academic/all/
The academy (in physics at least), is crusty and traditional, but not to the point of ignoring good work. It's like alternative medicine, do you think if essential oils cured cancer you wouldn't have all the big pharma companies leaping from their high horses?
Wolfram does some cool stuff with cellular automata, and has lots of students doing cool stuff too. What he's not done, neither with NKS nor anything since, is make some contribution to understanding the physical universe that was significant in eyes other than his own.
If wellknown land management practices could cure the decline of soil health, would big ag suddenly change its tune?
I've never been in a physics dept, but the parts of the academy I have seen absolutely would (and do) ignore good work if it's inconvenient or somehow unpalatable. This is of course, though not exclusively, related to the marriage of academy and industry.
No comment on the merit of Wolfram's work.
Insurance companies would, no? They're got every incentive to reduce payments to pharma companies.
I think experimental physics is always looking for theories that explain what they see, but theoretical physics hasn't delivered in the last few decades and the people employed doing theoretical physics have mostly succeeded at a political game, not a scientific one.
> It's like alternative medicine, do you think if essential oils cured cancer you wouldn't have all the big pharma companies leaping from their high horses?
There are effective chemicals offered in Europe that are not offered in the US. Sunblock is better outside the US for example. This is because of pharmaceutical interests and the US regulatory framework (which are really the same thing). If an essential oil cured cancer, I agree that word would get out, but the idea that things that work in any capacity for a specific ailment are automatically adopted by whatever corporation deals in that ailment is just not true.
Yes, and I think there is a success criterion that most people are not considering, which is: success as a less complicated explanation for the same phenomenon.
When people ask for new testable predictions as the only way a new theory can be successful, they are revealing that they don't consider parsimonious explanations to be a scientific goal.
Stephen's work with hypergraphs shows a lot of promise as a simple theory that implies other successful theories of physics. It focuses on emergent phenomenon that exhibit "pockets of computational reproducibility". The behavior of those pockets can then be predicted with tools in the physics canon like Riemannian geometry or complex numbers.
It doesn't have to be new testable predictions, but it should at least reproduce some testable predictions of the conventional theories.
As far as I know, these discrete graph models have been shown to reproduce some broad features of QM and GR (mostly the work of Jonathan Gorard rather than Wolfram), but they don't make any actual numerical predictions, which in my view is a basic requirement of a physical theory.
At the moment it seems like some intriguing toy models, similar in many respects to t'Hooft's cellular automaton model of QM, but there's no physical theory here
Other physicists engage with his money, I’ll agree to that.
He is a crank, but he’s too wealthy to be ignored by most academic physicists.
And the next few unknown values, BBλ(37).. BBλ(39) will be easier to determine too since the search space is smaller and no so-called cryptids have been identified yet (terms whose halting behaviour is closely related to unsolved math problems).
But if the effort that is being applied to researching BB(6) and BB(7), is applied to researching BBλ(37) and beyond, then we expect to run into similar difficulties of having more and more unsolved terms which do not lead to a normal form in any reasonable number of steps and also defy known techniques for proving them to lack a normal form.
There's some hope though that we'll be able to identify BBλ(49) before identifying BB(7). And while the former is known to exceed Graham's Number, the latter is only conjectured to do so, and I made a large bet with the people conjecturing it saying it won't be proven within 10 years.
And here's a readable and fascinating post on "the largest number that's representable in 64 bits": https://tromp.github.io/blog/2023/11/24/largest-number.
If you go through these and find some interesting things, it'd be worth posting to HN.