that took a while to get into, but it's really a beautiful system. however, the only advantage over a more classic notation system is temporary - you can always get more complex. Sure, "a h b" is more elegant than (~a & ~b) | (~a & b) | (a & ~b) (and there's probably a more elegant way to write that classically than what i did) but how much more complex is some long string of z's s's, h's etc. than its "expansion" in classic symbols? either way there's going to be parsing involved (the human kind). Also, I think this is a little bit dog wagging - he seems to think that if we had these symbols a concept like "a h b" would be as intuitive as "a & b" is. I don't think that's necessarily true. I think the simple operators we typically use are used because those are more obvious concepts, and just packaging up an advanced concept in a nice writing system doesn't make it easier to understand. but the symbols he chose are very elegant.

This is wonderful:
"I also like the fact that one’s interaction with my notation is literally hands-on and physical, rather than just all in your head. Knowledge shouldn’t be disconnected from the body. The body should be used as much as possible as a part of the means through which we acquire and store knowledge. Why can’t logic be like that too?"

I might be off base in making this analogy, but:
In the early days of synthesizers, as I understand it, there was an excitement about the fact that, by freeing music from the confines of the keyboard/rigid harmonic system, music making could become more egalitarian. Of course, this isn't exactly how it played out- early synthesizer music really turned into a specialty genre appealing only to the geekiest, the more adventurous end of the classical music spectrum, the delight of the avant garde. Synthesizers were really popularized when they stuck the keyboard back on them (I'm really not a scholar of this, but I imagine Moog fits into the picture somewhere around here) and they eventually ended up in Sears catalogues and under christmas trees or whatever. But interestingly, even though there's a bit of irony built into it, despite the keyboard a lot of the more intuitive aspects of controlling a synthesizer, and the fact that the thing could be automated so that you didn't actually have to play it, you could program it- ultimately it did lead to 'non-musicians' becoming 'important musicians'.

Point being, I agree Jon May that there isn't gonna be an explosion of lay logic comprehension all of a sudden, but you never know in the long haul exactly how developments such as this will play out.

One more point about that analogy- where Zellweger is proposing giving logic greater physicality, the synthesizer actually served to make music more mental, in a way, for the producer at least- since you're not actually playing the music in many cases so much as 'conceiving' it, turning different switches on and off more or less. There's a bunch that could be said against this point, but on a basic level it seems interesting to consider.

Sorry, forgive the self-indulgence, but one last thing having just finished the article, again relating to music-

"Of course, we can’t build anything in four dimensions,"

Probably setting myself up here, but: actually, I've been trying on an extremely amateur level, to try to conceive of music as a four-dimensional object for a little while now (only to feel the crushing blow of humility strike me within moments of the thought cropping up in my head). To acheive this I think would take a conceptual faculty I can't really imagine, but I find it really interesting to think about. Sound is material, after all.

okay, but how much music is in an object? if an entire piece it seems like there's way more than 4 dimensions. If a note, then music can be compared to any sonic signal, which i believe is something like amplitude and a polynomial to describe the frequency function (i, sadly, have never studied wave forms closely so somebody else might correct my error). Were you thinking of something more emotional/literary/arty?

Well, like I said, the crushing blow of humility...
But I'll give a shot at getting started- sure, way more than 4 dimensions to a whole piece, exactly, but doesn't he suggest the same about logic? And couldn't that be true of anything we perceive? I think it's maybe interesting that your immediate response about music is to say there's more than 4...
But I think it's valid to differentiate between a wave function that can be manifest as an audible signal and that signal when it is actually broadcast- pressure differentials, time function of sound/structural or conceptual framework of a constructed piece, the different physical behavior of different frequency ranges through space...

I try to make four out of the different behavior of different frequencies in terms of how it interacts with a given three dimensional space, plus the time component inherent in sound but enhanced by deliberate artistic decisions.