mission
My research into the golden ratio drew me to Euclid’s Elements. I only knew it by name prior. It has turned out to be a journey in itself. I was surprised to find that there is not one Elements. Like the Bible, there have been many translations and interpretations over the 2400 years since its creation. It’s been honored by some of the most beautiful publishings ever created. Some by hand, others by pushing the technology of the time. The editions of Adelard, Billingsley and Byrne have truly inspired me. And while some are critical of Heath’s edition, it doesn’t change the massive effort required - particularly in the typesetting - to make the work accessible to a contemporary audience.
It surprises me that Heath’s edition appears to be the end of the line. Why in a hundred years has no one picked it up again? All the efforts since then have essentially been a rework of Heath such as Joyce, Fitzpatrick, etc. If you search Elements on Amazon, there is mostly poorly produced renditions - particularly the digital editions. 20th century books on Geometry, such as Coxeter and Altshiller-Court, while wonderful and scholarly, drop one into the middle of a world of complexity without a firm foundation.
As you have said, Elements is not a book about geometry. I have seen it as a catalog of the logical relationships that our human minds can relay as truth. I believe that if presented well, it can be understood by anyone. Even children (maybe even more so). We know that Euclid is not the inventor of much of what is in Elements. He is an archivist, or, maybe better, an encyclopedist. Even so, the thought of bringing order to over 400 propositions on papyrus scrolls is staggering. Even with computers, the task is daunting. To maintain the dependencies, he would have had to have known it all in his mind.
How many have known Elements in its entirety? Perhaps more in antiquity than in our current age. I started building euclid.geometor.com as a framework for my own study. I was able to parse the XML of the Heath edition on the Perseus Project and incorporate it into my PHOTON platform. I want to formalize into a true semantic digital archive, where the information is detached from the presentation, giving it flexibility to be represented in many form factors, as well as providing a solid framework for metadata, taxonomies, and dependency graphs.
We are also not limited by the static nature of the print editions of the past. Constructive geometry is an art of motion in time. It is sequences of operations. Our technology today to allows us to communicate in this way. If done well and creatively, every proposition can be demonstrated without words.
I think there is a tremendous opportunity before us. Euclid has been on the mind of many recently. In addition to yourself, Wildberger and Wolfram have been bringing it up. Wolfram wrote this article a year ago - very enlightening: https://writings.stephenwolfram.com/2020/09/the-empirical-metamathematics-of-euclid-and-beyond/
I think Project Euclid can be approached in several iterations. The low hanging fruit for a first phase is a quality revision of the Heath edition - particularly as an ebook. It is in the public domain so there are no rights issues. I have the framework for the content set. With reasonable effort we can bring this out as a revenue generator to pursue the next phase - Elements 2.0 - a complete refactoring of the work into code-like structures that drive an animation and analytical engine.
goals
22.356 - Welcome
first log entry for the system