Wolfram Computation Meets Knowledge

5,000 Demonstrations: The Time to Go Interactive Is Now

Today we passed a remarkable milestone: the 5,000th Demonstration was published by the Wolfram Demonstrations Project, the free, interactive resource we created in 2007.

Selections from the Wolfram Demonstrations Project

Patterns from Math Rules Using Complex Numbers Quick Return Mechanism Table of Nuclides

This makes the Demonstrations Project the largest collection of open, instructional applets anywhere. And it’s also much needed proof that you can create a viable and vibrant technical publishing ecosystem based on interactive applications rather than dead documents—pivotal to moving technical communication into a major new era.

What’s the significance of this?

Over the last decade there has been massive change in the way we communicate most kinds of information. Yet one area had remained remarkably untouched: technical ideas. Whether in math textbooks, scientific papers, or commercial presentations, the format has not changed much since the 17th century. Formulas are still presented as static objects that you can’t compute from directly. Plots and diagrams are chosen slices of what are usually far richer underlying datasets. Write-ups pick special cases to illustrate conclusions, often without sufficient data for reproducing the results.

Some of this has moved from paper to electronic form, from monochrome 2D charts to 3D color—or, if you’re lucky, even an animation—but it’s still a one-way information flow from writer to reader that’s static and low bandwidth.

Imagine instead that the author sets up an exploratory environment for the topic, theory, or proposal in question. You interact with their ideas—formulas, graphics, or datasets—and challenge them with your choice of parameters; you discover the example cases that interest you, not just follow what the author thinks is important; you live their ideas, not just have them explained. Rather than going down a railroad track, the authors have set a multidimensional space for you to navigate as you please.

That exactly describes a “Demonstration”, a form of exposition we launched two years ago.

A typical (if a long way from the most exciting) example is my diffraction grating exploration. Traditionally you have physics books about diffraction that tell you what happens if you change the slit width, color of the light you’re diffracting, and so on. The authors of such books presented their knowledge in words and pictures—perhaps now animations—for you to read. Instead, my Demonstration communicates my knowledge about diffraction gratings as an interactive space that you, as the reader, can explore with an infinite combination of multiple parameter values.

Diffraction Grating Intensities

The Demonstrations website contains interactive models like this from almost every imaginable area of technical endeavor—sciences, engineering, economics, and business, to name a few. Some are from teachers, for education, or from their students engaged in projects. Some are supplements to traditional journal papers. And some are unique research results first presented as Demonstrations.

Is this really so new? There have been countless ideas for making education interactive, and dozens of bold new plans to teach math or science in a better way. But that’s just it: they have remained radical but unrealized, or incremental but ineffective.

The Demonstrations Project is radical and realized. With 5,000 Demonstrations, it already has a huge amount of content. (And of course, 5,000 fully functioning knowledge spaces cover far more than 5,000 textbook pages of pictures and text. How many traditional pages would you need to achieve the same?) With over 6 million Demonstrations used from around the world (with the source code of many viewable, too), it’s already one of the most used instructional applet sites.

Importantly, most of these 5,000 came from outside Wolfram Research, contributed by a growing community of professors, engineers, doctors, teachers and students, lawyers and bankers, and artists and musicians from around the world. Not programmers per se, but authors able to express their knowledge in a compelling new medium.

So why has the Demonstrations Project turned into such a viable, vibrant, interactive publishing community while so many others haven’t gotten off the ground?

The simple answer is just one Mathematica command: Manipulate.

Think of Manipulate as automation for interface building. It takes parameters, figures out which element best represents each, lays them out, and immediately generates an applet all-in-one. Its key achievement is to make interactivity so easy and so instant that it can be part of anyone’s everyday workflow. (Traditional environments involve a lot of manual construction like creating objects, setting up event functions, and labeling and positioning controls before getting to the subject matter.) Just like making a static business chart became everyday with spreadsheets, so making an application to represent ideas has become everyday with Manipulate.

And it really can be very quick (as shown in our screencast “Creating an Application in 60 Seconds“). I was at a math education conference in London listening to a talk that showed some animations of a boat crossing a river with different current flows. I was speaking soon after, but before I did, another attendee handed me a USB key with an interactive version of the boat. (It was Mathematica educator Phil Ramsden.) He’d built it in real time during the boat-featured talk. People were amazed when I showed it in my talk and explained its rapid, recent production.

In truth, it’s not just Manipulate that’s made the Demonstrations Project possible but a suite of technologies. Mathematica provides the underlying language and user interface technology, and is the development environment for creating Demonstrations. Mathematica Player is a free downloadable application that runs Demonstrations and interactive applets created in Mathematica by accessing the computational power of Mathematica.

So one key reason for the Demonstrations Project’s success is new technology. Simply put, it prevents authors from losing a lot of creative energy as implementational heat (and frustration!) when publishing their knowledge interactively. Creating Demonstrations is quick, fun, and rewarding for authors, which goes a long way toward explaining why we have 5,000 of them versus just a handful for interactive education projects based on older technologies.

Another aspect of the Demonstrations Project is the set of choices we’ve made for the publishing framework, which we chose to create with the new, interactive technology in Mathematica. It is run like a journal, with submissions reviewed by experts to ensure reliability, trustworthiness, and consistency between examples. And by design, all submissions are limited to one interactive panel with limited explanatory text around it.

But this is by no means the only way Mathematica interactivity can be deployed. Instead, documents containing a mixture of text, graphics, formulas, and multiple interactive elements can be used for many new technical communication models. Mathematica notebook documents blur the line between traditional documents and applications, providing unique, new hybrid experiences. (Because I’m a physicist, I describe this document-application duality in terms of particle-wave duality in my blog post “The Day That Documents and Applications Merged“.)

In the end, the real game-changer is this: traditional technical information providers finally have a new model to work from that’s both highly innovative and established. The Demonstrations Project is significant in its own right, but it’s also a proof of concept of where Mathematica-based content can take us.

Will textbook publishers rise to the challenge? Or will entirely new enterprises be our new educational content providers? With states from Texas to California forcing textbooks to go electronic, the time to go live and interactive is surely now.


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  1. yes. still,
    it feels like there is no program to test usability and didactical value of those demonstrations,
    or integrate them in courses on those fields such as diffraction of linear algebra or what have you. this would require, i think, to pay the authors of existing books to ‘go interactive’. in mathematics, some books are better not changed, it takes you a few month but then you know some projective geometry etcetera.

    also, pricing is a problem for me, because it is not open authors basically have to buy mathematica and also buy for conversion if they want to make money with their ideas.

    so some will fear someone is pulling the strings, somewhere.

    i am excited to explore this as a lisp-like programming environment but feel unsure about its use in classroom.

    perhaps something to try integrated with an ‘open’ course on mathematics?

  2. How to prove “Manipulate Anything” in a Mathematica Way ?


    Because, Everything is an expression.

    And, Manipulate [ expression, {u, min, max}]

    So, Manipulate…… Anything !!!

  3. Demonstrations and interactive notebooks are valuable teaching resources. They enable teachers to demonstrate concepts in real time. They also help students to learn through the direct manipulation of parameters. Demonstrations and interactive notebooks do for mathematics what actual laboratory demonstrations do for science experiments. That is, they make mathematical concepts more tangible to students. Interactive books are the logical culmination of these two technologies.

  4. Come docente di Matematica e Fisica sono molto lieto di esprimere un parere, consentitemi in Italiano, sulla eccezzionalità delle Demonstrations da simulare con Mathematica Player. Ritengo che esse siano una delle rivoluzioni informatiche più utili e meravigliose che condizioneranno tutti gli studenti e gli insegnanti delle scienze dell’epoca digitale. Io le uso sempre per le mie lezioni e suggerisco a tutti di capirle ed approfondirle. Grazie a Wolfram!
    Mileto Graziano

  5. great post!!!
    Thanks for sharing

  6. I’ve made some demonstration about diffraction, and uploaded three to the Wolfram Demonstrations Project website.
    I’ve made several demonstartions like Conrad Wolfram, but I had no time to upload them until now.




    Gabor Angler
    Physics student
    Eotvos University
    Hungary, Budapest

  7. I do like Demonstration Project very much, spatially for educational purposes, but as soon as a particular model becomes slightly complex it requires too many machine recourses and the figures stop too evolve smoothly in the screen. This makes it hard to manage in front of a populated class

  8. Dear mathematematicians from Wolfram Blog I have an interesting site to make research on him.It was on Terry Tao blog

  9. I am a HUGE fan of Wolfram Demonstrations. They are a source of fascination and wonder to me. I often use them as inspiration for my own programming in Mathematica. I would LOVE a place where users and developers can swap useful Mathematica code outside of Demonstrations. I think it would benefit everyone and make it easier for developers/users of Mathematica to do things in general.

  10. theartistpoet,

    We encourage all members of the Mathematica community to share their work with other Mathematica users by contributing items to the Wolfram Library Archive.

    Click here to submit material:

    Thanks for writing,

    The Wolfram Blog Team

  11. This is great news. Although Wolfram is still young, I think it will revolutionize the web as we know it,