Counterpoint: he notes our techniques are based on writing, but it goes deeper: our symbolic writing (including mathematical notation) is based on speech, for which we have dedicated linguistic structures in our brains, much as we have a visual center. It is deep-seated, and many have argued fundamentally entwined with sapience. Thus, even if it's not theoretically the best way, it might be the best way
for us. But I'm going to argue it
is the theoretically best way:
Linguistic descriptions have a key advantage over pictorial in that they represent or reference rather than show. This enables them to be compact, and omit unnecessary detail. (Of course, showing rather than telling is a strength of visual representation).
Yes, you can have a hierarchy of visual systems, and zoom-in or hide. But a fundamental problem here I think is in choosing the hierarchy - that is, the way the system is modularized.
Different modularizations of the same system are often appropriate for different uses of that system, or for considering different aspects of it. For even a slightly complex system, there are a huge number of different modularizations possible, and not all of them are useful. Often, you'll start with a poor one, and eventually have insights moving you towards the ideal one. (Of course, sometimes the "right" modularization is obvious, especially for well-known families of problems).
All this is very difficult. My point is that it is easier to switch modularities linguistically than pictorially, by changing your concepts. Without the right modularity, it's difficult to pictorially show just the aspects of interest instead of the whole picture. In contrast, one can linguistically omit detail by referencing it (implicitly, as a separate module).
Maybe it's possible to do this visually, though I suspect it thereby would have become linguistic!
[Though the above is a counterpoint, I'm very impressed with the talk. He's working both ends of abstraction, with concrete working software demonstrating cool useful practical techniques that, while not universal, would be helpful in many domains; and also framing it within, and using it to illustrate, the deep universal and philosophical idea of unthinkable thoughts. BTW e.g. uncomputable numbers.]