One only has to watch a baby on the subway, trying to move a magazine illustration as if it were an iPad, to realize that the rest of us are far from escaping the crippling influence of typewriters on notation. In a different universe the Lascaux cave paintings came to life long ago, without being forced through the eye of the linear text needle. In a different universe we've already spent millennia coming to terms with alien notation that is entirely graphic. This is not that universe.
While I admire this experimental effort, it's a first draft transliteration of the linear typewriter text. If there were a Darwinian pool of thousands of visual alternatives, this would not be the system that survived. I have two thoughts on how one could progress, here. First, imagine visual systems from the ground up, drawing from the best role models across the sciences. Why are Richard Feynman's diagrams considered absolute genius? Learn enough topology to browse their visual systems, with a focus on those that have broken free of their representational origins, reveling in new rules for how adjacent shapes can dance. Second, develop an iPad computer language that one can program with one finger, never typing. Make it more productive than Richard Stallman on Emacs. One will need the visual equivalent to syntax-aware editing, so every gesture is meaningful, no gesture is wasted. View the human user as neural net, arbitrarily trainable, and let all notation evolve and simplify. Ideally, have a neural net actually evolve the interface and notation in evolution with human users; it won't have our preconceptions as to what "needs to be there." Most new notations suffer from adoption anxiety. We all dream of that language that takes half a lifetime to master, but rewards us with many lifetimes of productivity. (Haskell is as close as civilization has come to this, so far.) Yet we walk away from something new like this if we can't figure it out quickly. My objection is that this notation suffers from being way too literal. Arbitrary adjacent shapes can acquire arbitrary meaning; don't be afraid to explore this.
