The Theory Works!

The equation that Albert Einstein wrote down for the gravitational field in 1915 is simple enough:

But working out its consequences is not. And in fact even after 100 years we’re still just at the beginning of the process.

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Note added 07/31/20: Some information regarding Wolfram Cloud products described in this post may be outdated. Please visit https://www.wolfram.com/cloud to learn more.

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Six and a half years ago we put Wolfram|Alpha and the sophisticated computational knowledge it delivers out free on the web for anyone in the world to use. Now we’re launching the Wolfram Open Cloud to let anyone in the world use the Wolfram Language—and do sophisticated knowledge-based programming—free on the web.

It’s been very satisfying to see how successfully Wolfram|Alpha has democratized computational knowledge and how its effects have grown over the years. Now I want to do the same thing with knowledge-based programming—through the Wolfram Open Cloud.

Last week we released Wolfram Programming Lab as an environment for people to learn knowledge-based programming with the Wolfram Language. Today I’m pleased to announce that we’re making Wolfram Programming Lab available for free use on the web in the Wolfram Open Cloud.
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I think it was 1979 when I first met Marvin Minsky, while I was still a teenager working on physics at Caltech. It was a weekend, and I’d arranged to see Richard Feynman to discuss some physics. But Feynman had another visitor that day as well, who didn’t just want to talk about physics, but instead enthusiastically brought up one unexpected topic after another.

That afternoon we were driving through Pasadena, California—and with no apparent concern to the actual process of driving, Feynman’s visitor was energetically pointing out all sorts of things an AI would have to figure if it was to be able to do the driving. I was a bit relieved when we arrived at our destination, but soon the visitor was on to another topic, talking about how brains work, and then saying that as soon as he’d finished his next book he’d be happy to let someone open up his brain and put electrodes inside, if they had a good plan to figure out how it worked.

Feynman often had eccentric visitors, but I was really wondering who this one was. It took a couple more encounters, but then I got to know that eccentric visitor as Marvin Minsky, pioneer of computation and AI—and was pleased to count him as a friend for more than three decades.
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I’m excited today to be able to announce the launch of Wolfram Programming Lab—an environment for anyone to learn programming and computational thinking through the Wolfram Language. You can run Wolfram Programming Lab through a web browser, as well as natively on desktop systems (Mac, Windows, Linux).

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(New York Public Library)

Ada Lovelace was born 200 years ago today. To some she is a great hero in the history of computing; to others an overestimated minor figure. I’ve been curious for a long time what the real story is. And in preparation for her bicentennial, I decided to try to solve what for me has always been the “mystery of Ada”.

It was much harder than I expected. Historians disagree. The personalities in the story are hard to read. The technology is difficult to understand. The whole story is entwined with the customs of 19th-century British high society. And there’s a surprising amount of misinformation and misinterpretation out there.

But after quite a bit of research—including going to see many original documents—I feel like I’ve finally gotten to know Ada Lovelace, and gotten a grasp on her story. In some ways it’s an ennobling and inspiring story; in some ways it’s frustrating and tragic.

It’s a complex story, and to understand it, we’ll have to start by going over quite a lot of facts and narrative.

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An Elementary Introduction to the Wolfram Language is available in print, free on the web, etc.

I wasn’t sure if I was ever going to write another book. My last book—A New Kind of Science—took me more than a decade of intensely focused work, and is the largest personal project I’ve ever done.

But a little while ago, I realized there was another book I had to write: a book that would introduce people with no knowledge of programming to the Wolfram Language and the kind of computational thinking it allows.

The result is An Elementary Introduction to the Wolfram Language, published today in print, free on the web, etc. Continue reading

A hundred years ago today Albert Einstein published his General Theory of Relativity—a brilliant, elegant theory that has survived a century, and provides the only successful way we have of describing spacetime.

There are plenty of theoretical indications, though, that General Relativity isn’t the end of the story of spacetime. And in fact, much as I like General Relativity as an abstract theory, I’ve come to suspect it may actually have led us on a century-long detour in understanding the true nature of space and time.

I’ve been thinking about the physics of space and time for a little more than 40 years now. At the beginning, as a young theoretical physicist, I mostly just assumed Einstein’s whole mathematical setup of Special and General Relativity—and got on with my work in quantum field theory, cosmology, etc. on that basis.

But about 35 years ago, partly inspired by my experiences in creating technology, I began to think more deeply about fundamental issues in theoretical science—and started on my long journey to go beyond traditional mathematical equations and instead use computation and programs as basic models in science. Quite soon I made the basic discovery that even very simple programs can show immensely complex behavior—and over the years I discovered that all sorts of systems could finally be understood in terms of these kinds of programs.

Encouraged by this success, I then began to wonder if perhaps the things I’d found might be relevant to that ultimate of scientific questions: the fundamental theory of physics. Continue reading

Not many years ago, the idea of having a computer broadly answer questions asked in plain English seemed like science fiction. But when we released Wolfram|Alpha in 2009 one of the big surprises (not least to me!) was that we’d managed to make this actually work. And by now people routinely ask personal assistant systems—many powered by Wolfram|Alpha—zillions of questions in ordinary language every day.

It all works fairly well for quick questions, or short commands (though we’re always trying to make it better!). But what about more sophisticated things? What’s the best way to communicate more seriously with AIs? Continue reading

Today is the 200th anniversary of the birth of George Boole. In our modern digital world, we’re always hearing about “Boolean variables”—1 or 0, true or false. And one might think, “What a trivial idea! Why did someone even explicitly need to invent it?” But as is so often the case, there’s a deeper story—for Boolean variables were really just a side effect of an important intellectual advance that George Boole made.

When George Boole came onto the scene, the disciplines of logic and mathematics had developed quite separately for more than 2000 years. And George Boole’s great achievement was to show how to bring them together, through the concept of what’s now called Boolean algebra. And in doing so he effectively created the field of mathematical logic, and set the stage for the long series of developments that led for example to universal computation.

When George Boole invented Boolean algebra, his basic goal was to find a set of mathematical axioms that could reproduce the classical results of logic. His starting point was ordinary algebra, with variables like x and y, and operations like addition and multiplication.

At first, ordinary algebra seems a lot like logic. After all, p and q is the same as q and p, just as p×q = q×p. But if one looks in more detail, there are differences. Like p×p = p², but p and p is just p. Somewhat confusingly, Boole used the notation of standard algebra, but added special rules to create an axiom system that he then showed could reproduce all the usual results of logic.

Boole was rather informal in the way he described his axiom system. But within a few decades, it had been more precisely formalized, and over the course of the century that followed, a few progressively simpler forms of it were found. And then, as it happens, 15 years ago I ended up finishing this 150-year process, by finding—largely as a side effect of other science I was doing—the provably very simplest possible axiom system for logic, that actually happens to consist of just a single axiom.

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“What is this a picture of?” Humans can usually answer such questions instantly, but in the past it’s always seemed out of reach for computers to do this. For nearly 40 years I’ve been sure computers would eventually get there—but I’ve wondered when.

I’ve built systems that give computers all sorts of intelligence, much of it far beyond the human level. And for a long time we’ve been integrating all that intelligence into the Wolfram Language.

Now I’m excited to be able to say that we’ve reached a milestone: there’s finally a function called ImageIdentify built into the Wolfram Language that lets you ask, “What is this a picture of?”—and get an answer.

And today we’re launching the Wolfram Language Image Identification Project on the web to let anyone easily take any picture (drag it from a web page, snap it on your phone, or load it from a file) and see what ImageIdentify thinks it is:

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