The Most-Used Mathematical Algorithm Idea in History
An octillion. A billion billion billion. That’s a fairly conservative estimate of the number of times a cellphone or other device somewhere in the world has generated a bit using a maximum-length linear-feedback shift register sequence. It’s probably the single most-used mathematical algorithm idea in history. And the main originator of this idea was Solomon Golomb, who died on May 1—and whom I knew for 35 years.
Solomon Golomb’s classic book Shift Register Sequences, published in 1967—based on his work in the 1950s—went out of print long ago. But its content lives on in pretty much every modern communications system. Read the specifications for 3G, LTE, Wi-Fi, Bluetooth, or for that matter GPS, and you’ll find mentions of polynomials that determine the shift register sequences these systems use to encode the data they send. Solomon Golomb is the person who figured out how to construct all these polynomials.
He also was in charge when radar was first used to find the distance to Venus, and of working out how to encode images to be sent from Mars. He introduced the world to what he called polyominoes, which later inspired Tetris (“tetromino tennis”). He created and solved countless math and wordplay puzzles. And—as I learned about 20 years ago—he came very close to discovering my all-time-favorite rule 30 cellular automaton all the way back in 1959, the year I was born. Continue reading
Fifty years ago today there was a six-year-old at a kindergarten (“nursery school” in British English) in Oxford, England who was walking under some trees and noticed that the patches of light under the trees didn’t look the same as usual. Curious, he looked up at the sun. It was bright, but he could see that one side of it seemed to be missing. And he realized that was why the patches of light looked odd.
He’d heard of eclipses. He didn’t really understand them. But he had the idea that that was what he was seeing. Excited, he told another kid about it. They hadn’t heard of eclipses. But he pointed out that the sun had a bite taken out of it. The other kid looked up. Perhaps the sun was too bright, but they looked away without noticing anything. Then the first kid tried another kid. And then another. None of them believed him about the eclipse and the bite taken out of the sun.
Edited transcript of a talk given on March 4, 2016, at the Computer History Museum, Mountain View, California.
I normally spend my time trying to build the future. But I find history really interesting and informative, and I study it quite a lot. Usually it’s other people’s history. But the Computer History Museum asked me to talk today about my own history, and the history of technology I’ve built. So that’s what I’m going to do here. Continue reading
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. Continue reading
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. Continue reading
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).
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.
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.