I think people have mostly stopped taking Stephen Wolfram very seriously. He did some great work early in his career, at CalTech and the Institute for Advanced Study, and (with a certain amount of intellectual property mess) went on to create *Mathematica*, which was and is very cool.

Then in 1992 he disappeared into a garret or something for a decade, and came out with the massive *A New Kind of Science*, which got a lot of attention because it was Wolfram after all, but which turned out to be basically puffery. And a certain amount of taking credit for other people’s earlier work.

Being wealthy and famous, however, and one imagines rather surrounded by yes-folks, Wolfram continues in the *New Kind of Science* vein, writing down various things that sound cool, but don’t appear to mean much (as friend Steve said when bringing the current subject to my attention, “Just one, single, testable assertion. That’s all I ask”).

The latest one (or a latest one) appears to be “The Ruliad”. Wolfram writes:

I call it the ruliad. Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways.

It’s not clear to me what “entangled” could mean there, except that it’s really complicated if you try to draw it on a sheet of paper. But “the result of following all possible computational rules in all possible ways” is pretty clearly isomorphic to (i.e. the same thing as) the set of all possible strings. Which is to say, the set of all possible books, even the infinitely-long ones.

(We can include all the illustrated books by just interpreting the strings in some XML-ish language that includes SVG. And it’s probably also isomorphic to the complete graph on all possible strings; that is, take all of the strings, and draw a line from each one to all of the others. Or the complete graph on the integers. Very entangled! But still the same thing for most purposes.)

Now the set of all possible strings is a really amazing thing! It’s incomprehensibly huge, even if we limit it to finite strings, or even finite strings that would fit in a reasonably-sized bound volume.

And if we do that latter thing, what we have is the contents of the Universal Library, from Borges’ story “The Library of Babel”. As that story notes, the Library contains

*All* — the detailed history of the future, the autobiographies of the archangels, the faithful catalog of the Library, thousands and thousands of false catalogs, the proof of the falsity of those false catalogs, a proof of the falsity of the *true* catalog, the gnostic gospel of Basilides, the commentary upon that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book into every language, the interpolations of every book into all books, the treatise Bede could have written (but did not) on the mythology of the Saxon people, the lost books of Tacitus.

Borges — The Library of Babel

It also contains this essay, and *A New Kind of Science*, and every essay Wolfram will ever write on “the Ruliad”, as well as every possible computer program in every language, every possible finite-automaton rule, and to quote Wolfram “the result of following all possible computational rules in all possible ways.” (We’ll have to allow infinite books for that one, but that’s a relatively simple extension, heh heh.)

So, it’s very cool to think about, but does it tell us anything about the world? (Spoiler: no.) Wolfram writes, more or less correctly:

it encapsulates not only all formal possibilities but also everything about our physical universe—and everything we experience can be thought of as sampling that part of the ruliad that corresponds to our particular way of perceiving and interpreting the universe.

and sure; for any fact about this particular physical universe (or, arguably, any other) and anything that we experience, the Library of Babel, the set of all strings, the complete graph on all strings, “the Ruliad”, contains a description of that fact or experience.

Good luck finding it, though. :)

This is the bit that Wolfram seems to have overlooked, depending on how you read various things that we writes. The set of all strings definitely contains accurate statements of the physical laws of our universe; but it also contains vastly more *inaccurate* ones. Physicists generally want to know which are which, and “the Ruliad” isn’t much help with that.

Even philosophers who don’t care that much about which universe we happen to be in, still want *correct* or at least *plausible* and *coherent* arguments about the properties of formal systems, or the structure of logic, or the relationship between truth and knowledge, and so on; the Universal Library / “Ruliad” does contain lots of those (all of them, in fact), but it provides no help in finding them, or in differentiating them from the obviously or subtly incorrect, implausible, and incoherent ones.

There is certainly math that one can do about the complete graph over the set of all strings, and various subgraphs of that graph. But that math will tell you very little about the propositions that those strings express. It’s not clear that Wolfram realizes the difference, or realizes just how much the utter generality of “the Ruliad” paradoxically simplifies the things one can say about it.

For instance, one of the few examples that Wolfram gives in the essay linked above, of something concrete that one might study concerning “the Ruliad” itself, is:

But what about cases when many paths converge to a point at which no further rules apply, or effectively “time stops”? This is the analog of a spacelike singularity—or a black hole—in the ruliad. And in terms of computation theory, it corresponds to something decidable: every computation one does will get to a result in finite time.

One can start asking questions like: What is the density of black holes in rulial space?

It somewhat baffles me that he can write this. Since “the Ruliad” represents the outputs of all possible programs, the paths of all possible transition rules, and so on, there *can be no* fixed points or “black holes” in it. For any point, there are an infinite number of programs / rules that map that point into some other, different point. The “density of black holes in rulial space” is, obviously and trivially, exactly zero.

He also writes, for instance:

A very important claim about the ruliad is that it’s unique. Yes, it can be coordinatized and sampled in different ways. But ultimately there’s only one ruliad.

Well, sure, there is exactly one Universal Library, one set of all strings, one complete graph on the integers. This is, again, trivial. The next sentence is just baffling:

And we can trace the argument for this to the Principle of Computational Equivalence. In essence there’s only one ruliad because the Principle of Computational Equivalence says that almost all rules lead to computations that are equivalent. In other words, the Principle of Computational Equivalence tells us that there’s only one ultimate equivalence class for computations.

I think he probably means something by this, well maybe, but I don’t know what it would be. Obviously there’s just one “result of following all possible computational rules in all possible ways”, but it doesn’t take any Principle of Computational Equivalence to prove that. I guess maybe if you get to the set of all strings along a path that starts at one-dimensional cellular automata, that Principle makes it easier to see? But it’s certainly not necessary.

He also tries to apply terminology from “the Ruliad” to various other things, with results that generally turn out to be trivial truths when translated into ordinary language. We have, for instance:

Why can’t one human consciousness “get inside” another? It’s not just a matter of separation in physical space. It’s also that the different consciousnesses—in particular by virtue of their different histories—are inevitably at different locations in rulial space. In principle they could be brought together; but this would require not just motion in physical space, but also motion in rulial space.

What is a “location in rulial space”, and what does it mean for two things to be at different ones? In ordinary language, two things are at different points in “rulial space” if their relationships to other things are not the same; which is to say, they have different properties. (Which means that separation in physical space is in fact *one kind* of separation in “rulial space”, we note in passing.) So this paragraph says that one human consciousness can’t get inside another one, because they’re different in some way. And although you might somehow cause them to be completely identical, well, I guess that might be hard.

This does not seem like a major advance in either psychology or philosophy.

Then he gets into speculation about how we might be able to communicate between “different points in rulial space” by sending “rulial particles”, which he identifies with “concepts”. The amount of hand-waving going on here is impressive; Steve’s plea for a falsifiable claim is extremely relevant. In what way could this possibly turn out to be wrong?

(It can, on the other hand, easily turn out to be not very useful, and I think so far it’s doing a good job at that.)

He also proceeds, hands still waving at supersonic speed, to outline a Kantian theory that says that, although “the Ruliad” contains all possible laws of physics, we seem to live in a universe that obeys only one particular set of laws. This, he says, is because “for observers generally like us it’s a matter of abstract necessity that we must observe general laws of physics that are the ones we know”.

What “observers like us” means there is just as undefined as it was when Kant wrote the same thing only with longer German words. He goes on like this for some time, and eventually writes:

People have often imagined that, try as we might, we’d never be able to “get to the bottom of physics” and find a specific rule for our universe. And in a sense our inability to localize ourselves in rulial space supports this intuition. But what our Physics Project seems to rather dramatically suggest is that we can “get close enough” in rulial space to have vast predictive power about how our universe must work, or at least how observers like us must perceive it to work.

which is basically just gibberish, on the order of “all we have to do is find the *true* physics text in the Universal Library!”.

It’s hard to find anyone but Wolfram writing on “the Ruliad” (or at least I haven’t been able to), but the Wolfram essay points to an arxiv paper “Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types” by two authors associated with Wolfram Research USA (one also associated with Pompeu Fabra University in Barcelona, and the other with the University of Cambridge in Cambridge, and one does wonder what those institutions think about this). That paper notably does not contain the string “Ruliad”. :)

I may attempt to read it, though.