Remixing Euclid | Opensource.com

Remixing Euclid

Posted 12 Jan 2011 by 

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As we struggle towards a world of remixable educational content, one of the oft-expressed fears is that the remixers will confuse and damage perfectly good resources. Is this a reasonable fear? What would Euclid say?

When we talk about geometry, the vast majority of us are actually talking about what mathematicians now call, more precisely, Euclidean geometry. And why do they call it Euclidean geometry? Because the Greek mathematician Euclid laid out its foundations in a manuscript about 2400 years ago, and mathematicians have been nodding their heads in agreement ever since.

Euclid's Elements made its way from Alexandria to Athens, to Rome, to Baghdad, back to Europe, and around the globe. In days gone by, one could not be considered properly educated without having studied Euclid. Until the 20th Century, Elements was the second most printed book in the world, ahead of Shakespeare and behind only the Bible. It is said that country lawyer Abe Lincoln carried a copy from town to town so that he could study its proofs by candlelight. Einstein called it "the holy little geometry book".

Our understanding of many academic topics continue to evolve -- in some cases rapidly. Euclidean geometry, however, is not one of these cases.

It's no exaggeration to say that the compasses and straightedges we used in our geometry classes in school were functionally identical to those used by the Greeks, with construction techniques described in Euclid's proofs more than two millenia ago. Every illustration from every elementary geometry textbook can be reasonably considered a direct derivative of Euclid's work.

Sounds like the very epitome of public domain, doesn't it?

Which is what makes it so fascinating that a Google search for "Euclid's Elements" yields, for its first three hits, links to David E. Joyce's interpretation of Euclid's Elements -- which have a prominent notice assigning copyright to Professor Joyce, and his employer Clark University, on every single page.

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Copyright by Default and What it Means

We live in a world of copyright. In countries that are members of the Berne Convention (which is almost all of them), it's no longer necessary even to claim copyright; copyright is simply assumed, and creators of works must make a conscious effort if they wish to put those works into any kind of commons. Which means there's no sense in blaming Professor Joyce. When he first put his site on the internet in 1997, the copyleft debate was in its infancy even as it pertained to code, and licenses like Creative Commons simply did not exist.

It's a funny thing about the public domain: anybody can take any work in the public domain, remix it to their heart's content, and release it as their own, and they magically become copyright holders of that new work -- even if it were orginally 99.9% someone else's work. Absolutely legal. Want to take a Jane Austen novel and turn it into a regency zombie thriller? Knock yourself out. Want to turn Tolstoy into steampunk? No problem.

It therefore makes perfect sense that there should be tons of proprietary derivatives of Euclid's work. It's the oldest textbook in the world, it's a complete encapsulation of its subject matter, and it's completely free to be pilfered. What's not to like? There's every incentive to take things from the public domain, and zero incentive to put anything back. Which explains, in part, why it's surprisingly difficult to find a useful version of Elements in the public domain.

There's the Joyce version, which is comprehensive and extremely well annotated; to modern readers, succinct definitions like "a line is breadthless length" can certainly benefit from a bit of exposition, and Joyce does that well. Trouble is, it's all under a very strict license, which means that creating and distributing derivative works without consent would be forbidden -- and the Java applets, which are much of the value-add, are outdated and fail to load on many modern browsers.  There's also the interactive text from the Perseus Digital Library at Tufts, which provides the entire text of the Sir Thomas Heath translation, including commentary, in HTML and XML, with extensive internal hyperlinks. Also great, but lacking in useful illustrations, and made available through a somewhat restrictive Creative Commons license with a non-commercial clause. The versions that are truly public domain are scanned PDFs of various editions, of varying quality, and not easily consumable by most would-be Euclidean disciples.

And then there are the thousands of elementary geometry textbooks out there, all of which are, by very definition, derivative works of Euclid -- and are sold at a much higher price point than "free on the internet". What about those? How much money do taxpayers spend to purchase endless derivative works based on a public domain text that was the gold standard of scholarship for more than 2000 years?

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Why Give Back?

It's true that there are improvements to be made on Euclid's Elements: in style, if not in substance. It's true that different kids learn differently, and that different teachers teach differently -- and there may well be room for dozens of geometry textbooks, all geared towards particular learning styles and needs.

But that's not what happens in our schools. Districts choose a single text judged to be "best", and hand that text to every student, regardless of learning style or distinct needs. The teacher is expected to bridge all gaps between text and student, which is fair -- but they have to rely upon their own wits to find the resources to help them to bridge those gaps, which seems distinctly unfair. Of course, it's always been that way: our educational system comes from the industrial revolution, and at that time the factory school was the only conceivable mechanism for achieving quality education at scale.

That's not true anymore. More and more smart people are starting to question the effectiveness of the factory model of education -- watch Sir Ken Robinson's brilliant RSA video, for example -- and as the educational ecosystem expands into the digital world, new potential contributors are joining the ecosystem. It's not just professional educators, either: small education startups, homeschooling parents, passionate bystanders, and even motivated self-learners are all potential creators of educational content. The more we can do to keep that ecosystem open, and the lower the barriers for new entrants to add to the ecosystem, the more innovation we'll see.

Open Ecosystems = More Innovation

The ecosystem of open source software exploded once it reached a critical mass. Suddenly, it was no longer necessary to purchase expensive coding tools, and it was no longer necessary to be a "professional"; anyone with an idea and some basic computer skill could find a good base of code, grab it, read some tutorials on the internet, and start running. And because that commons was designed from the beginning to expand, software innovation based on open source software accelerated, and continues to accelerate today.

Getting to that critical mass of open educational resources continues to be a challenge. The resources must be good enough to be useful, and open enough to be extensible. There are lots of efforts to build those resources from scratch, but building quality educational materials from scratch is not easy.

Which is why it's important to take copious advantage of every good resource that already does exist. Euclid wrote the definitive geometry textbook for us, 2500 years ago. That's hard. Now, writing a Javascript widget that illustrates one of Euclid's propositions? That's easy, at least by comparison -- something that a clever hacker parent could do in a weekend. And if a dozen clever parents get together, ol' Euclid takes on new life. And if those parents decide to put that code goes into the commons, it stays there -- for good.

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Greg DeKoenigsberg is the Vice President of Community for Eucalyptus Systems, the pioneering open source cloud company. He is responsible for leading the company's relationship with the broader open source community. Greg brings to Eucalyptus over a decade of open source advocacy and community leadership, with the majority of this time spent building and leading communities for open source leader Red Hat. While at Red Hat, Greg served in various community leadership roles, including senior

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