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Computational Thinking

Education & Academic

Online Enrichment with Free Daily Study Groups

Students are spending countless hours online for classes this year, pushing educators to offer more engaging and worthwhile virtual content. We debuted Wolfram Daily Study Groups in early April with this in mind, and the results have far surpassed our expectations! Throughout this ongoing program, we’ve been able to keep students, professionals and lifelong learners engaged and connected in an enriching online community. With several Study Groups completed, and more in the works, we thought we’d share some of our successes so far.

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How Odd Was the Full Moon on Halloween 2020? Once in a Blue Moon and a Lifetime!

Halloween this year had a surprise up its sleeve. In rare celestial serendipity, the night of costume metamorphosis also featured a full moon, which helped to conjure the spooky mood. Because it might have been the first and last full-moon Halloween that some people witnessed in their lifetime (cue ominous music), I think it was significantly underrated. Moreover, it was the day of a blue moon (the second full moon within a month), but that is not a surprise, as any Halloween’s full moon is always a blue moon. The Moon’s color did not change, though, at least for those away from the smoke of volcanos and forest fires that are capable of turning it visibly blue. To appreciate the science and uniqueness of a full moon this Halloween, I built this visualization that tells the whole story in one picture. This is how I did it.

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The Winners of the 2020 One-Liner Competition

Although this year’s Wolfram Technology Conference was virtual, that didn’t stop us from running the ninth annual One-Liner Competition, where attendees vie to produce the most amazing results they can with 128 or fewer characters of Wolfram Language code. Here are the winners, including an audio game, a hands-free 3D viewer and code that makes up countries.

Computation & Analysis

Playing Cards with Alice and Bob: Using Secure Multi‑Party Computation and the Wolfram Language to Determine a Winner

While catching up with my old friends Alice and Bob on Zoom a few days ago, I became intrigued by their recent card game hobby—and how they used the Wolfram Language to settle an argument. To figure out who gets to go first at the start of the game, they take one suit (spades) from a full deck, and each draws a card. Then, the person with the highest card value wins. Because they are using only one suit, there can be no ties. Simple, right?

Current Events & History

Tackling a Pandemic: A Computer-Based Maths Approach

How did the Department of Health and Social Care (DHSC) come up with their multi-phase response to tackle COVID-19? In this post, I investigate how the UK government's original plan against the coronavirus aligns with the four-step computational thinking process. Teachers are welcome to use this post as a free resource.

Please note: where possible, I have taken data from before the DHSC's plan was published.

The Computational Thinking Process

What is the computational thinking process? Simply put, it is a sequence of four steps that you can take in order to solve a problem. The aim is not just to obtain a solution, but to ensure that the right choices were made, the right tools were used and the right outcomes were achieved along the way. The steps are as follows: you define explicitly the problem you wish to solve, abstract it to a computational form, compute an answer, then interpret the result:

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Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful

I Never Expected This

It’s unexpected, surprising---and for me incredibly exciting. To be fair, at some level I've been working towards this for nearly 50 years. But it’s just in the last few months that it’s finally come together. And it’s much more wonderful, and beautiful, than I’d ever imagined.

In many ways it's the ultimate question in natural science: How does our universe work? Is there a fundamental theory? An incredible amount has been figured out about physics over the past few hundred years. But even with everything that's been done---and it's very impressive---we still, after all this time, don't have a truly fundamental theory of physics.

Back when I used do theoretical physics for a living, I must admit I didn't think much about trying to find a fundamental theory; I was more concerned about what we could figure out based on the theories we had. And somehow I think I imagined that if there was a fundamental theory, it would inevitably be very complicated.

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Bring the Classroom Home with Free Projects, Computational Explorations and Other Resources

Communities the world over are bracing themselves for impact from the novel coronavirus COVID-19. Many school districts in particular have already suspended sessions for several weeks to come—and understandably, parents and educators feel anxious about navigating at-home learning (among the variety of other concerns brought about by a pandemic!).

Professionally, a large part of what I do at Wolfram involves working with educators, students and organizations, and empowering them with the technology to think computationally. I know of several parents with older kids who are now at home, enrolled in schools that are not completely prepared to provide online instruction. While the internet is awash with curricula, it can be a challenging task to assess the quality, relevance and usefulness of each course, given the amount of what is out there.

For decades now at Wolfram, we’ve been committed to the creation of cutting-edge technology and resources for classrooms. Let’s take a look at our wealth of free online resources for quality education while at home.
Education & Academic

Hitting All the Marks: Exploring New Bounds for Sparse Rulers and a Wolfram Language Proof

The sparse ruler problem has been famously worked on by Paul Erdős, Marcel J. E. Golay, John Leech, Alfréd Rényi, László Rédei and Solomon W. Golomb, among many others. The problem is this: what is the smallest subset of so that the unsigned pairwise differences of give all values from 1 to ? One way to look at this is to imagine a blank yardstick. At what positions on the yardstick would you add 10 marks, so that you can measure any number of inches up to 36?

Another simple example is of size 3, which has differences , and . The sets of size 2 have only one difference. The minimal subset is not unique; the differences of also give .

Part of what makes the sparse ruler problem so compelling is its embodiment in an object inside every schoolchild's desk—and its enduring appeal lies in its deceptive simplicity. Read on to see precisely just how complicated rulers, marks and recipes can be.