Kindergarden Quantum Mechanics Graduates
We&#x27;re near a visual turning point.<p>Conventional math notation coevolved with prevailing display technologies, from cold type to early serial computer interactions. It took a generation for people to learn to chat on a phone, and a generation for the shift from typewriters to word processors to change how people compose text. It will take a similar generation drawing on a digital tablet to change how people compose mathematical thought. However, teaching through a pandemic, this evolution has been radically accelerated.<p>Apps like Notability fluidly replace blackboards for teaching on Zoom. They however are primitive drawing editors. One outgrows them like a beginner windsurfing board. Apps pioneered by digital artists such as architects support much more advanced algorithmic drawing. Concepts is my current favorite; an example of math notes in Concepts is here: <a href="https:&#x2F;&#x2F;www.math.columbia.edu&#x2F;~bayer&#x2F;S21&#x2F;Combinatorics&#x2F;Week7&#x2F;Feb23.pdf" rel="nofollow">https:&#x2F;&#x2F;www.math.columbia.edu&#x2F;~bayer&#x2F;S21&#x2F;Combinatorics&#x2F;Week7...</a><p>Still, these are closed editors. Unlike Emacs, they can&#x27;t be used to modify themselves. One longs here for Lisp-universe live drawings, a break from the misconception that a static final visually appealing canvas is the objective. Rather, how much thought can we externalize and reify as live doodles? What notion of space will replace artboards and layers, for supporting drawings as live computation, completely accessible as if one had a time-traveling functional programming debugger?<p>When software supports this, crosses that threshold like a general purpose programming language where users can create arbitrary modifications and extensions in this visual medium, then we&#x27;ll see more papers like the present.