We call it “Spikey”, and in my life today, it’s everywhere:
It comes from a 3D object—a polyhedron that’s called a rhombic hexecontahedron:
But what is its story, and how did we come to adopt it as our symbol?
Logic is a foundation for many things. But what are the foundations of logic itself?
In symbolic logic, one introduces symbols like p and q to stand for statements (or “propositions”) like “this is an interesting essay”. Then one has certain “rules of logic”, like that, for any p and any q, NOT (p AND q) is the same as (NOT p) OR (NOT q).
But where do these “rules of logic” come from? Well, logic is a formal system. And, like Euclid’s geometry, it can be built on axioms. But what are the axioms? We might start with things like p AND q = q AND p, or NOT NOT p = p. But how many axioms does one need? And how simple can they be?
It was a nagging question for a long time. But at 8:31pm on Saturday, January 29, 2000, out on my computer screen popped a single axiom. I had already shown there couldn’t be anything simpler, but I soon established that this one little axiom was enough to generate all of logic:
But how did I know it was correct? Well, because I had a computer prove it. And here’s the proof, as I printed it in 4-point type in A New Kind of Science (and it’s now available in the Wolfram Data Repository):
On June 23 we celebrate the 30th anniversary of the launch of Mathematica. Most software from 30 years ago is now long gone. But not Mathematica. In fact, it feels in many ways like even after 30 years, we’re really just getting started. Our mission has always been a big one: to make the world as computable as possible, and to add a layer of computational intelligence to everything.
Our first big application area was math (hence the name “Mathematica”). And we’ve kept pushing the frontiers of what’s possible with math. But over the past 30 years, we’ve been able to build on the framework that we defined in Mathematica 1.0 to create the whole edifice of computational capabilities that we now call the Wolfram Language—and that corresponds to Mathematica as it is today.
From when I first began to design Mathematica, my goal was to create a system that would stand the test of time, and would provide the foundation to fill out my vision for the future of computation. It’s exciting to see how well it’s all worked out. My original core concepts of language design continue to infuse everything we do. And over the years we’ve been able to just keep building and building on what’s already there, to create a taller and taller tower of carefully integrated capabilities.
It’s fun today to launch Mathematica 1.0 on an old computer, and compare it with today:
The more one does computational thinking, the better one gets at it. And today we’re launching the Wolfram Challenges site to give everyone a source of bite-sized computational thinking challenges based on the Wolfram Language. Use them to learn. Use them to stay sharp. Use them to prove how great you are.
The Challenges typically have the form: “Write a function to do X”. But because we’re using the Wolfram Language—with all its built-in computational intelligence—it’s easy to make the X be remarkably sophisticated.
The site has a range of levels of Challenges. Some are good for beginners, while others will require serious effort even for experienced programmers and computational thinkers. Typically each Challenge has at least some known solution that’s at most a few lines of Wolfram Language code. But what are those lines of code?
It was 1968. I was 8 years old. The “space race” was in full swing. For the first time, a space probe had recently landed on another planet (Venus). And I was eagerly studying everything I could to do with space.
Then on April 3, 1968 (May 15 in the UK), the movie 2001: A Space Odyssey was released—and I was keen to see it. So in the early summer of 1968 there I was, the first time I’d ever been in an actual cinema (yes, it was called that in the UK). I’d been dropped off for a matinee, and was pretty much the only person in the theater. And to this day, I remember sitting in a plush seat and eagerly waiting for the curtain to go up, and the movie to begin.
It started with an impressive extraterrestrial sunrise. But then what was going on? Those weren’t space scenes. Those were landscapes, and animals. I was confused, and frankly a little bored. But just when I was getting concerned, there was a bone thrown in the air that morphed into a spacecraft, and pretty soon there was a rousing waltz—and a big space station turning majestically on the screen.
What happens if you take four of today’s most popular buzzwords and string them together? Does the result mean anything? Given that today is April 1 (as well as being Easter Sunday), I thought it’d be fun to explore this. Think of it as an Easter egg… from which something interesting just might hatch. And to make it clear: while I’m fooling around in stringing the buzzwords together, the details of what I’ll say here are perfectly real.
Last September we released Version 11.2 of the Wolfram Language and Mathematica—with all sorts of new functionality, including 100+ completely new functions. Version 11.2 was a big release. But today we’ve got a still bigger release: Version 11.3 that, among other things, includes nearly 120 completely new functions.
This June 23rd it’ll be 30 years since we released Version 1.0, and I’m very proud of the fact that we’ve now been able to maintain an accelerating rate of innovation and development for no less than three decades. Critical to this, of course, has been the fact that we use the Wolfram Language to develop the Wolfram Language—and indeed most of the things that we can now add in Version 11.3 are only possible because we’re making use of the huge stack of technology that we’ve been systematically building for more than 30 years.
We’ve always got a large pipeline of R&D underway, and our strategy for .1 versions is to use them to release everything that’s ready at a particular moment in time. Sometimes what’s in a .1 version may not completely fill out a new area, and some of the functions may be tagged as “experimental”. But our goal with .1 versions is to be able to deliver the latest fruits of our R&D efforts on as timely a basis as possible. Integer (.0) versions aim to be more systematic, and to provide full coverage of new areas, rounding out what has been delivered incrementally in .1 versions.
In addition to all the new functionality in 11.3, there’s a new element to our process. Starting a couple of months ago, we began livestreaming internal design review meetings that I held as we brought Version 11.3 to completion. So for those interested in “how the sausage is made”, there are now almost 122 hours of recorded meetings, from which you can find out exactly how some of the things you can now see released in Version 11.3 were originally invented. And in this post, I’m going to be linking to specific recorded livestreams relevant to features I’m discussing.
OK, so what’s new in Version 11.3? Well, a lot of things. And, by the way, Version 11.3 is available today on both desktop (Mac, Windows, Linux) and the Wolfram Cloud. (And yes, it takes extremely nontrivial software engineering, management and quality assurance to achieve simultaneous releases of this kind.) Continue reading
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.