Marten Kuilman has written extensively on four-folds and what he calls quadralectics, division-thinking, or four-fold thinking.

Publishing in the Netherlands, his books aren’t available on Amazon. Graciously, he has made several of his works available on the internet via his blogs Quadralectics and Quadriformisratio. Quadriformisratio presents Four – A Rediscovery of the ‘Tetragonus Mundus’, a treatise of four-folds through history, and Quadralectics is his two volume work on Quadralectic Architecture.

Not only does Kuilman expound at length on various four-folds throughout the ages and how they affected the intellectual and artistic developments of the time, his work unifies many of them into his four aspects of visibility: invisible invisibility, invisible visibility, visible visibility, and visible invisibility. Above, I’ve arranged these four aspects by my positions for the four elements. Unfortunately, they aren’t in the same sequence as Kuilman’s quadrants.

Because Kuilman emphasizes a recurring association of  his four-fold of visibility with communication, it is also reminiscent of Hjelmslev’s Net. Then, invisibility could be understood as content, and visibility as expression.

Interestingly, my four-fold of Bright-to-Dark (here or here) is most relatable to this four-fold of visibility, but in the reverse sense that the invisible invisibility is bright, and the visible visibility is dark. One could quickly reconcile this opposition by considering the empty circle as most invisible, and the full circle as most visible.

Another interesting result of Kuilman’s investigations is to derive his four-fold of Unity, Muun (Multi-unity), Part, and Whole, which I believe has important associations with my four-fold Structure-Function.

References:

Marten Kuilman / Four – A Rediscovery of the ‘Tetragonus Mundus’

Marten Kuilman / QUADRALECTIC ARCHITECTURE – A Panoramic Review

http://quadriformisratio.wordpress.com/

http://quadralectics.wordpress.com/

http://quadralectics.wordpress.com/7-the-quadralectic-theory/

[*8.48, *8.52, *8.53, *8.54, *8.55]

<>