Computational Foundations for the Second Law of Thermodynamics

Computational Foundations for the Second Law of Thermodynamics

The Mystery of the Second Law

Entropy increases. Mechanical work irreversibly turns into heat. The Second Law of thermodynamics is considered one of the great general principles of physical science. But 150 years after it was first introduced, there’s still something deeply mysterious about the Second Law. It almost seems like it’s going to be “provably true”. But one never quite gets there; it always seems to need something extra. Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. But the mystery of the Second Law has never gone away.

Why does the Second Law work? And does it even in fact always work, or is it actually sometimes violated? What does it really depend on? What would be needed to “prove it”?

For me personally the quest to understand the Second Law has been no less than a 50-year story. But back in the 1980s, as I began to explore the computational universe of simple programs, I discovered a fundamental phenomenon that was immediately reminiscent of the Second Law. And in the 1990s I started to map out just how this phenomenon might finally be able to demystify the Second Law. But it is only now—with ideas that have emerged from our Physics Project—that I think I can pull all the pieces together and finally be able to construct a proper framework to explain why—and to what extent—the Second Law is true. Continue reading

A 50-Year Quest: My Personal Journey with the Second Law of Thermodynamics

When I Was 12 Years Old…

I’ve been trying to understand the Second Law now for a bit more than 50 years.

It all started when I was 12 years old. Building on an earlier interest in space and spacecraft, I’d gotten very interested in physics, and was trying to read everything I could about it. There were several shelves of physics books at the local bookstore. But what I coveted most was the largest physics book collection there: a series of five plushly illustrated college textbooks. And as a kind of graduation gift when I finished (British) elementary school in June 1972 I arranged to get those books. And here they are, still on my bookshelf today, just a little faded, more than half a century later:

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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

The Basic Arc of the Story

As I’ve explained elsewhere, I think I now finally understand the Second Law of thermodynamics. But it’s a new understanding, and to get to it I’ve had to overcome a certain amount of conventional wisdom about the Second Law that I at least have long taken for granted. And to check myself I’ve been keen to know just where this conventional wisdom came from, how it’s been validated, and what might have made it go astray.

And from this I’ve been led into a rather detailed examination of the origins and history of thermodynamics. All in all, it’s a fascinating story, that both explains what’s been believed about thermodynamics, and provides some powerful examples of the complicated dynamics of the development and acceptance of ideas. Continue reading

Wolfram|Alpha as the Way to Bring Computational Knowledge Superpowers to ChatGPT

See also:
“What Is ChatGPT Doing … and Why Does It Work?” »

Wolfram|Alpha as the Way to Bring Computational Knowledge Superpowers to ChatGPT

ChatGPT and Wolfram|Alpha

It’s always amazing when things suddenly “just work”. It happened to us with Wolfram|Alpha back in 2009. It happened with our Physics Project in 2020. And it’s happening now with OpenAI’s ChatGPT. Continue reading

The Latest from Our R&D Pipeline: Version 13.2 of Wolfram Language & Mathematica

Exploring Wolfram Language 13.2 with Stephen Wolfram

The Latest from Our R&D Pipeline: Version 13.2 of Wolfram Language & Mathematica

Delivering from Our R&D Pipeline

In 2020 it was Versions 12.1 and 12.2; in 2021 Versions 12.3 and 13.0. In late June this year it was Version 13.1. And now we’re releasing Version 13.2. We continue to have a huge pipeline of R&D, some short term, some medium term, some long term (like decade-plus). Our goal is to deliver timely snapshots of where we’re at—so people can start using what we’ve built as quickly as possible. Continue reading

Launching Version 13.1 of Wolfram Language & Mathematica 🙀🤠🥳

Exploring Wolfram Language 13.1 with Stephen Wolfram

The Epic Continues…

Last week it was 34 years since the original launch of Mathematica and what’s now the Wolfram Language. And through all those years we’ve energetically continued building further and further, adding ever more capabilities, and steadily extending the domain of the computational paradigm.

In recent years we’ve established something of a rhythm, delivering the fruits of our development efforts roughly twice a year. We released Version 13.0 on December 13, 2021. And now, roughly six months later, we’re releasing Version 13.1. As usual, even though it’s a “.1” release, it’s got a lot of new (and updated) functionality, some of which we’ve worked on for many years but finally now brought to fruition. Continue reading

Alien Intelligence and the Concept of Technology

The Nature of Alien Intelligence

“We’re going to launch lots of tiny spacecraft into interstellar space, have them discover alien intelligence, then bring back its technology to advance human technology by a million years”. I’ve heard some pretty wacky startup pitches over the years, but this might possibly be the all-time winner.

But as I thought about it, I realized that beyond the “absurdly extreme moonshot” character of this pitch, there’s some science that I’ve done that makes it clear that it’s also fundamentally philosophically confused. The nature of the confusion is interesting, however, and untangling it will give us an opportunity to illuminate some deep features of both intelligence and technology—and in the end suggest a way to think about the long-term trajectory of the very concept of technology and its relation to our universe.

Let’s start with a scenario. Let’s say one of the little spacecraft comes across a planet where it sees complicated swirling patterns:

The Jupiter Great Red Spot

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Games and Puzzles as Multicomputational Systems

Games and Puzzles as Multicomputational Systems

Humanizing Multicomputational Processes

Multicomputation is one of the core ideas of the Wolfram Physics Project—and in particular is at the heart of our emerging understanding of quantum mechanics. But how can one get an intuition for what is initially the rather abstract idea of multicomputation? A good approach, I believe, is to see it in action in familiar systems and situations. And I explore here what seems like a particularly good example: games and puzzles. Continue reading

Twenty Years Later: The Surprising Greater Implications of A New Kind of Science

Twenty Years Later: The Surprising Greater Implications of A New Kind of Science

From the Foundations Laid by A New Kind of Science

When A New Kind of Science was published twenty years ago I thought what it had to say was important. But what’s become increasingly clear—particularly in the last few years—is that it’s actually even much more important than I ever imagined. My original goal in A New Kind of Science was to take a step beyond the mathematical paradigm that had defined the state of the art in science for three centuries—and to introduce a new paradigm based on computation and on the exploration of the computational universe of possible programs. And already in A New Kind of Science one can see that there’s immense richness to what can be done with this new paradigm. Continue reading

The Making of A New Kind of Science

The Making of A New Kind of Science

I Think I Should Write a Quick Book…

In the end it’s about five and a half pounds of paper, 1280 pages, 973 illustrations and 583,313 words. And its creation took more than a decade of my life. Almost every day of my thirties, and a little beyond, I tenaciously worked on it. Figuring out more and more science. Developing new kinds of computational diagrams. Crafting an exposition that I wrote and rewrote to make as clear as possible. And painstakingly laying out page after page of what on May 14, 2002, would be published as A New Kind of Science.

I’ve written before (even in the book itself) about the intellectual journey involved in the creation of A New Kind of Science. But here I want to share some of the more practical “behind the scenes” journey of the making of what I and others usually now call simply “the NKS book”. Some of what I’ll talk about happened twenty years ago, some more like thirty years ago. And it’s been interesting to go back into my archives (and, yes, those backup tapes from 30 years ago were hard to read!) and relive some of what finally led to the delivery of the ideas and results of A New Kind of Science as truckloads of elegantly printed books with striking covers. Continue reading