Spoken.page is a research project with the aim of making university and research level mathematics come alive on the internet, to experiment with new formats and presentations, to encourage the performance of mathematics and not just its production and print publication.Let us begin with three simple observations.
1. Reading maths papers is hard.
When an expert picks up a new paper on a particular topic, they might quickly see the new idea in Lemma 6 and the small tweak to definition 3 and understand what consequences it has for the main theorem. When a beginner picks up the same paper, it can be impenetrable. One must wade through a lot of boiler plate. This is very inefficient and frustrating.
We have found that occasionally a maths paper is significantly easier to understand, if a friend who really knows the material is reading the paper aloud for you. Where you had been confused before, the exact same words and the exact same symbols when read alound now suddenly "click". Just noting where the reader decides to place emphasis, where to speed up/slow down etc. can make all the difference. Wouldn't it be nice if a paper on the internet could read itself to you? i.e. if the page is built up bit by bit as someone reads it.
Simply handing a beginning student a published paper (or even just an arXiv article) is like teaching music students how to read notes and then handing them a score of Beethoven's 9th, expecting them to figure out on their own just how great it is.
Great maths, like music, should be performed.
...and this applies beyond just reading papers:
2. Video Lectures are hard to follow.
Since we can't all be expected to learn everything from reading papers, we go to class. Lectures and Seminars are designed to make material acessible to the learner. Indeed one of the features of a good speaker is that they highlight the important bits while glossing over the "unimportant" details. The most important thing is narrative. Pedants will note of course that _everything_ is logically/formally important, but it is not necessarily conducive to conveying the gist, the insight that makes a theory work.
In recent years universities have begun making video recordings of their classes available on the internet. This is to be applauded. However my experience is that it is much harder to follow a lecture on video than it is to follow the same lecture in person - sitting in the lecture hall. When whatching the video one looses concentration, the mind wanders. It is extremely tiring. Whatever the precise reasons, the truth is that blackboard lectures are a not a format that is optimised for the internet. Journal articles are optimised for print & archival, and lectures are optimised for in person learning. Our goal is to find a new format sitting between print and video that is optimised for online consuption.
3. There is no maths format native to the internet.
PDFs are a format imported from the world of print media, videos are imported from classrooms. There are experiments on new formats (interactive software, games, videos, animations) especially at the middle and highschool level, but nothing compelling has emerged so far. And I am specifically also talking about university level mathematics here, all the way from standard coursework to research papers.
3b. There's more than just maths.
Whatever we learn in this project will undoubtedly have applications in other fields.
What we would like to do here is the twofold:
Firstly, to begin our experiments, we would like to create a few trial videos using the manim.community software (known from 3blue1brown) but instead of focusing on clever animations for individual examples, focus primarily on presenting text and LaTeX, and on conveying much more content - i.e. entire courses.
Experimentation should include questions like:
Beyond just coding new maths content using manim, we can imagine expanding the manim library itself to make it easier to make our type of text-based maths video and maybe even adapt manim for use in live talks at conferences (see also here) as a bridge for onboarding mathematicians to our project.
Secondly, we ought to think beyond video; to move away from 'video' as a format altogether. There is something unsatisfying about having a video render a page of text - resulting in text on the screen that is not clickable, not highlightable, not copyable. The real format should be somewhere between a text document and a video. Do we need a custom app or can this be achieved using html5 wizardry? Indeed purely CSS animations might be up to the task. We should explore other possible outputs for manim code, or even other animation engines entirely such as reanimate or liqvidjs.org?
It should also be possible to make the narrative flow of a lecture non-linear and interactive - a choose-your-own-adventure if you will - to allows you to enter into, or skip past extra details according to your own needs. (See also here perhaps, or here). Finally, how can this whole endavour be more cooperative? Can we learn from the Wiki approach to editing?
In the end, we should have a better idea for what works and what does not, how to best dynamically render maths text on a cellphone (vertical video?)? on a tablet? a computer? digital paper? How to make the creation of new content easier than it is currently? How to collectively curate a database of maths lectures, classes, courses and seminars? What is the best way for future academic publishing in the age of the internet? .. and how do the lessons learned here translate into other areas besides maths.
To begin, we break to project into distinct areas of expertise.
Content Curation (mathematicians/students):
The primary work consists of writing down a mathematical narrative - be it a paper or a lecture series, then subsequently to break it down into sequences of imagined animations paired with the corresponding to-be-spoken text. The end result might be compared to a storyboard for a movie.
At the end we could potentially prepare a recording of the spoken words or even record a rough version given as a blackboard talk.
Once the content has been thus curated, it is time to involve the animators and creators. We imagine there will be several rounds of back-and-forth here.
Content Creation (python scripting / video editing):
At this stage we decide on the visuals for the content - blackboard, notebook, computer terminal? Implement the relevant animations as video snippets in manim - mostly text and LaTeX with symbols appearing and animating in specific orders, but possibly including a handful of custom animations specific to the material. Once the raw material is ready, we must stich together the videos and the audio using video editing software and modifying timings accordingly. Finally we will render the output to multiple formats.
This process should quickly teach us what parts of manim work well for our purposes and which ones need tweaking / developing. Therefore we envision a side-project of:
Manim Development (python coding):
Dive into the internals of the manim.community library and adapt it to best suit our needs. Create a standard library of interfaces for our content creators to use.
Firstly, we should do research on the current landscape of maths education publishing. We should conduct a survey of maths publishing tools and programs available now and the companies operating in this space. We should aim to talk to a wide range of people in the mathematics education establishment about what they have been learning, where they see this space devloping.