Thanks Dimitri,
What I find interesting is his reference to numbers:
SA: Can you describe noncommutative geometry?
BG: Since the time of Descartes, we've found it very powerful to label points by their coordinates, either on Earth by their latitude and longitude or in threespace by the three Cartesian coordinates, x,yand z, that you learn in high school. And we've always imagined that those numbers are like ordinary numbers, which have the property that, when you multiply them togetherwhich is often an operation you need to do in physicsthe answer doesn't depend on the order of operation: 3 times 5 is 5 times 3.
What we seem to be finding is that when you coordinatize space on very small scales, the numbers involved are not like 3's and 5's, which don't depend upon the order in which they're multiplied.
There's a new class of numbers that do depend on the order of multiplication.

On my website:
http://www.mu6.com/numbers.html I describe this as a property of restructured spacetime (postulating that spacetime is an unbreakable and almost infinite elastic membrane).
The complexity of our 'reality' is just the macro and micro interacting spacetime layers which can push each other but also can couple and knot.
If we could buy such 'membrane material' today in KMart or GB ...we could build such concept in REALITY, today. This is a real physics world concept ... not magic. ;)