Multi-Way Causal Graphs by the independent theoretical physicist Stephen Wolfram; an attempt to unify physics with his own theory of Quantum Gravity.

With each node representing a superposition and every line a causal path, his intent is to reveal the "true" nature of what is traditionally known as a Fiber Bundle. His definition is titled 'Branchial Spaces.'

The rule used—that I call rule 30—is of exactly the same kind as before, and can be described as follows. First, look at each cell and its right-hand neighbor. If both of these were white on the previous step, then take the new color of the cell to be whatever the previous color of its left-hand neighbor was. Otherwise, take the new color to be the opposite of that.

The picture shows what happens when one starts with just one black cell and then applies this rule over and over again. And what one sees is something quite startling—and probably the single most surprising scientific discovery I have ever made. Rather than getting a simple regular pattern as we might expect, the cellular automaton instead produces a pattern that seems extremely irregular and complex.

That ChatGPT can automatically generate something that reads even superficially like human-written text is remarkable, and unexpected. But how does it do it? And why does it work? My purpose here is to give a rough outline of what’s going on inside ChatGPT—and then to explore why it is that it can do so well in producing what we might consider to be meaningful text. I should say at the outset that I’m going to focus on the big picture of what’s going on—and while I’ll mention some engineering details, I won’t get deeply into them. (And the essence of what I’ll say applies just as well to other current “large language models” [LLMs] as to ChatGPT.)

The first thing to explain is that what ChatGPT is always fundamentally trying to do is to produce a “reasonable continuation” of whatever text it’s got so far, where by “reasonable” we mean “what one might expect someone to write after seeing what people have written on billions of webpages, etc.”

So let’s say we’ve got the text “The best thing about AI is its ability to”. Imagine scanning billions of pages of human-written text (say on the web and in digitized books) and finding all instances of this text—then seeing what word comes next what fraction of the time. ChatGPT effectively does something like this, except that (as I’ll explain) it doesn’t look at literal text; it looks for things that in a certain sense “match in meaning”. But the end result is that it produces a ranked list of words that might follow, together with “probabilities”:

And the remarkable thing is that when ChatGPT does something like write an essay what it’s essentially doing is just asking over and over again “given the text so far, what should the next word be?”—and each time adding a word. (More precisely, as I’ll explain, it’s adding a “token”, which could be just a part of a word, which is why it can sometimes “make up new words”.)

But, OK, at each step it gets a list of words with probabilities. But which one should it actually pick to add to the essay (or whatever) that it’s writing? One might think it should be the “highest-ranked” word (i.e. the one to which the highest “probability” was assigned). But this is where a bit of voodoo begins to creep in. Because for some reason—that maybe one day we’ll have a scientific-style understanding of—if we always pick the highest-ranked word, we’ll typically get a very “flat” essay, that never seems to “show any creativity” (and even sometimes repeats word for word). But if sometimes (at random) we pick lower-ranked words, we get a “more interesting” essay.

Cellular automata are really interesting: Through the interplay of simple rules emerges fairly complex behavior, sometimes capable of universal computation.

They can also look really pretty: A few days ago, I came across some 1D cellular automata posters on Reddit. Sadly, the available images were way too tiny for printing and the author hasn’t yet posted the "high res print exports" supposedly "available soon" – so I took matters into my own hands by writing a poster generator in Python. With the help of Cairo, it generates arbitrarily scalable PDFs whose look is fairly customizable – the images above are screenshots of the generated PDFs.

Hope this is a nice early holiday present for you.

Today we bring to you a special gift from Stephen Wolfram himself: Conus Textile Shells!

A Blog by Stephen Wolfram

The Nature of the Problem

Let’s say we had a way to distribute beacons around our solar system (or beyond) that could survive for billions of years, recording what our civilization has achieved. What should they be like?

It’s easy to come up with what I consider to be sophomoric answers. But in reality I think this is a deep—and in some ways unsolvable—philosophical problem, that’s connected to fundamental issues about knowledge, communication and meaning.

Still, a friend of mine recently started a serious effort to build little quartz disks, etc., and have them hitch rides on spacecraft, to be deposited around the solar system. At first I argued that it was all a bit futile, but eventually I agreed to be an advisor to the project, and at least try to figure out what to do to the extent we can.

But, OK, so what’s the problem? Basically it’s about communicating meaning or knowledge outside of our current cultural and intellectual context. We just have to think about archaeology to know this is hard. What exactly was some arrangement of stones from a few thousand years ago for? Sometimes we can pretty much tell, because it’s close to something in our current culture. But a lot of the time it’s really hard to tell.

OK, but what are the potential use cases for our beacons? One might be to back up human knowledge so things could be restarted even if something goes awfully wrong with our current terrestrial civilization. And of course historically it was very fortunate that we had all those texts from antiquity when things in Europe restarted during the Renaissance. But part of what made this possible was that there had been a continuous tradition of languages like Latin and Greek—not to mention that it was humans that were both the creators and consumers of the material.

But what if the consumers of the beacons we plan to spread around the solar system are aliens, with no historical connection to us? Well, then it’s a much harder problem.