The Path to a New Paradigm

One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. But what I’ve increasingly been realizing is that actually it’s showing us something even bigger and deeper: a whole fundamentally new paradigm for making models and in general for doing theoretical science. And I fully expect that this new paradigm will give us ways to address a remarkable range of longstanding central problems in all sorts of areas of science—as well as suggesting whole new areas and new directions to pursue. Continue reading

Hiding in Plain Sight for a Century?

On December 7, 1920, Moses Schönfinkel introduced the S and K combinators—and in doing so provided the first explicit example of a system capable of what we now call universal computation. A hundred years later—as I prepared to celebrate the centenary of combinators—I decided it was time to try using modern computational methods to see what we could now learn about combinators. And in doing this, I got a surprise.

It’s already remarkable that S and K yield universal computation. But from my explorations I began to think that something even more remarkable might be true, and that in fact S alone might be sufficient to achieve universal computation. Or in other words, that just applying the rule

S f g x → f[x][g[x]]

over and over again might be all that’s needed to do any computation that can be done.

I don’t know for sure that this is true, though I’ve amassed empirical evidence that seems to point in this direction. And today I’m announcing a prize of $20,000 (yes, the “20” goes with the 1920 invention of combinators, and the 2020 making of my conjecture) for proving—or disproving—that the S combinator alone can support universal computation. Continue reading

Based on a talk at Numerous Numerosity: An interdisciplinary meeting on the notions of cardinality, ordinality and arithmetic across the sciences.

Everyone Has to Have Numbers… Don’t They?

The aliens arrive in a starship. Surely, one might think, to have all that technology they must have the idea of numbers. Or maybe one finds an uncontacted tribe deep in the jungle. Surely they too must have the idea of numbers. To us numbers seem so natural—and “obvious”—that it’s hard to imagine everyone wouldn’t have them. But if one digs a little deeper, it’s not so clear.

It’s said that there are human languages that have words for “one”, “a pair” and “many”, but no words for specific larger numbers. In our modern technological world that seems unthinkable. But imagine you’re out in the jungle, with your dogs. Each dog has particular characteristics, and most likely a particular name. Why should you ever think about them collectively, as all “just dogs”, amenable to being counted? Continue reading

Look What We Made in Five Months!

It’s hard to believe we’ve been doing this for 35 years, building a taller and taller tower of ideas and technology that allow us to reach ever further. In earlier times we used to release the results of efforts only every few years. But in recent times we’ve started doing incremental (“.1”) releases that deliver our latest R&D achievements—both fully fleshed out, and partly as “coming attractions”—much more frequently.

We released Version 12.2 on December 16, 2020. And today, just five months later, we’re releasing Version 12.3. There are some breakthroughs and major new directions in 12.3. But much of what’s in 12.3 is just about making Wolfram Language and Mathematica better, smoother and more convenient to use. Things are faster. More “But what about ___?” cases are handled. Big frameworks are more completely filled out. And there are lots of new conveniences.

There are also the first pieces of what will become large-scale structures in the future. Early functions—already highly useful in their own right—that will in future releases be pieces of major systemwide frameworks. Continue reading

In preparation for a conference entitled “Distributed Consensus with Cellular Automata & Related Systems” that we’re organizing with NKN (= “New Kind of Network”) I decided to explore the problem of distributed consensus using methods from A New Kind of Science (yes, NKN “rhymes” with NKS) as well as from the Wolfram Physics Project.

A Simple Example

&#10005 BlockRandom[SeedRandom[77]; Module[{pts = RandomPointConfiguration[HardcorePointProcess[0.09, 2, 2], Rectangle[{0, 0}, {40, 40}]]["Points"], clrs}, clrs = Table[ RandomChoice[{.65, .35} -> {Hue[0.15, 0.72, 1], Hue[ 0.98, 1, 0.8200000000000001]}], Length[pts]]; Graphics[{EdgeForm[Gray], Table[Style[Disk[pts[[n]]], clrs[[n]]], {n, Range[Length[pts]]}]}]]]

Consider a collection of “nodes”, each one of two possible colors. We want to determine the majority or “consensus” color of the nodes, i.e. which color is the more common among the nodes.

One obvious method to find this “majority” color is just sequentially to visit each node, and tally up all the colors. But it’s potentially much more efficient if we can use a distributed algorithm, where we’re running computations in parallel across the various nodes. Continue reading

See also:The Concept of the Ruliad (November 10, 2021)
(introducing the term “ruliad” for “rulial universe”)

What Is Formal, and What Is Actualized?

Why does the universe exist? Why is there something rather than nothing? These are old and fundamental questions that one might think would be firmly outside the realm of science. But to my surprise I’ve recently realized that our Physics Project may shed light on them, and perhaps even show us the way to answers.

We can view the ultimate goal of our Physics Project as being to find an abstract representation of what our universe does. But even if we find such a representation, the question still remains of why that representation is actualized: why what it represents is “actually happening”, with the actual stuff our universe is “made of”.

It’s one thing to say that we have a rule or program that can reproduce a representation of what our universe is doing. But it seems very different to say that the rule or program is “actually being run” and is “actually generating” the “physical reality” of our universe. Continue reading

How’s It Going?

When we launched the Wolfram Physics Project a year ago today, I was fairly certain that—to my great surprise—we’d finally found a path to a truly fundamental theory of physics, and it was beautiful. A year later it’s looking even better. We’ve been steadily understanding more and more about the structure and implications of our models—and they continue to fit beautifully with what we already know about physics, particularly connecting with some of the most elegant existing approaches, strengthening and extending them, and involving the communities that have developed them.

And if fundamental physics wasn’t enough, it’s also become clear that our models and formalism can be applied even beyond physics—suggesting major new approaches to several other fields, as well as allowing ideas and intuition from those fields to be brought to bear on understanding physics.

Needless to say, there is much hard work still to be done. But a year into the process I’m completely certain that we’re “climbing the right mountain”. And the view from where we are so far is already quite spectacular. Continue reading

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For most big ideas in recorded intellectual history one can answer the question: “What became of the person who originated it?” But late last year I tried to answer that for Moses Schönfinkel, who sowed a seed for what’s probably the single biggest idea of the past century: abstract computation and its universality.

I managed to find out quite a lot about Moses Schönfinkel. But I couldn’t figure out what became of him. Still, I kept on digging. And it turns out I was able to find out more. So here’s an update…. Continue reading

“What about Consciousness?”

For years I’ve batted it away. I’ll be talking about my discoveries in the computational universe, and computational irreducibility, and my Principle of Computational Equivalence, and people will ask “So what does this mean about consciousness?” And I’ll say “that’s a slippery topic”. And I’ll start talking about the sequence: life, intelligence, consciousness.

I’ll ask “What is the abstract definition of life?” We know about the case of life on Earth, with all its RNA and proteins and other implementation details. But how do we generalize? What is life generally? And I’ll argue that it’s really just computational sophistication, which the Principle of Computational Equivalence says happens all over the place. Then I’ll talk about intelligence. And I’ll argue it’s the same kind of thing. We know the case of human intelligence. But if we generalize, it’s just computational sophistication—and it’s ubiquitous. And so it’s perfectly reasonable to say that “the weather has a mind of its own”; it just happens to be a mind whose details and “purposes” aren’t aligned with our existing human experience. Continue reading