3D and 2D - one can physically hide content, the other forbids it.
3D and 2D - one can physically hide content, the other forbids it.

D-ness, the Beginning

I’ve been casually thinking about the world in terms of D-ness for decades. D-ness includes our familiar 2d3d4d. Never found much use for 1d. But do theoretical physicists?


The endearing physicist MIchio Kaku can entertain up to 11 spatiotemporal dimensions. He can write the mathematical proof. He’s a giant of highly-effective-people. I recommend wolfing down whatever you can locate of his books, videos, interviews.  (Michio Kaku Explains the 11 Dimensions of the Multiverse)


I have no notion what the implications of the next seven dimensions will have on the facts of my paltry few. But I have lots of thoughts about those common three. It started like this


When you practice collage you may find an ideal image of a spring green expanse of meadow, but it has an eyesore shack in it. Shack doesn’t say what you want, the meadow does. So you paste a sunset or vase or tiger over the shack. You disappear it. You paste whatever image says what you want to say paired with the meadow.


It’s very like poetry, finding the juicy word that nails it. Because the use of visual art is to communicate — and the rule here is you don’t use words.



Rules are important in creativity. I remember some poet writing that he composed a different form of verse every day (limerick, psalm) in his youth. He practiced the forms.


When I started making my own art — not the drawing/painting skills I’d thought I’d needed — I was knifing images from magazines and my own art books. My rules were: sourcing found-materials and using color harmony to bind my compositions.



And I had another rule — you could stand back and enjoy a strong abstraction, or you could move in and read the content. An observer cannot do both at once. So the work shifted meaning depending on where you positioned yourself.


That’s a rule I never once formulated. I discovered it by looking back at my work.


When I changed my media, using my own photographs — and ruled that they could only butt up against each other (no overlay, no hiding content). And in looking back at that I realized a fundamental truth. A mathematical truth.



Collage is a 3D medium. The ability for one image to obliterate another requires one to be above (in front of) another. It intervenes in space, same as a lady wearing a big hat in the theater seat ahead of you blocks the screen.


The photomosaics were rigorous grids of mostly 4×6 photographs from a regular printing shop. I took the photos, waited, then came home with dual stacks — double prints! — of images. I’d deal them out in piles and begin to discover how they went together. Always an adventure, like traveling to somewhere with new food, new manners, new breeds of ducks.


Well, working with the no-overlap rule meant that photomosaics were a 2D medium. I had the option of culling photos that didn’t work in my design, but I frowned on it. The more images in one work, the happier I was. My biggest was 13 feet of 4″x6″s. Kimono Lost in a Sand Garden.


As a side-note, a number of people remarked on the horse image in that work. I’ve never figured out where they see it.





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Sloan Nota collage

Love Lost by Sloan Nota, collage. Copyright Sloan Nota. via artist’s collection.

I discovered both myself and my art while making impromptu collages. Paper, x-acto and glue, books and magazines. Excellent images on paper more beautiful than newsprint. Later I moved on to photomosaics — images from my camera butted up in a tight grid. The grid form pushed me to create images which flowed across the grid lines and stole your attention from them. If you savored my image you could not focus on the grid, and vice versa.

I was playing with those two artforms far in the back of my mind when ‘click’ I saw the fundamental difference between them. Fundamental. Collage lets you paste a smaller image on a background image. If a tractor besmirches your glorious landscape, paste a swan on top of it.

Sloan Nota art

The Persistence of Memory, by Sloan Nota. Photomosaic (built from original photos of the Lions in Trafalgar Square, London). art copyright Sloan Nota. via the artist’s personal collection.

Collage is a 3d artform. Yes its made from materials commonly thought of as 2d, but when one image can block another that is a 3d phenomenon. Its not available to you in a photomosaic which gives the artist nowhere to hide the nasty bits — the off-tune detail that will skew the meaning of your completed work, the deodorant ad, the moldy vegetable.


Horse and rider from Horemheb's tomb, ca 1325 BC. via pinterest. https://www.pinterest.com/pin/59743132527643630/

Example of low relief.  Horse and rider from Horemheb’s tomb, ca 1325 BC. via pinterest.


'Grant',_bronze_sculpture, by William_Rudolf_O'Donovan; horse, _Thomas_Eakins. via https://en.wikipedia.org/wiki/Soldiers%27_and_Sailors%27_Arch#/media/File:%27Lincoln_and_Grant%27,_bronze_sculptures_by_William_Rudolf_O%27Donovan_(men)_%26_Thomas_Eakins_(horses),_1893-1894,_Grand_Army_Plaza,_Brooklyn,_New_York_City.JPG

Example of high relief. ‘General Grant, ‘ bronze sculpture, by William_Rudolf_O’Donovan (Grant); Thomas Eakins (horse).  via wikipedia.com.


Tang Horse and Rider, Chinese ceramic. via collectingchineseceramics

Example of fully 3d art, art in the round.  Tang Horse and Rider, Chinese ceramic. via collectingchineseceramics.


Here’s a quick synopsis of my view of the Dimensions. Not a physicist’s understanding but an instructive play with semantics.

This sheet of business paper is the epitome of 2D, yes, width x length. But what if the paper’s for watercolorists? Then it has dimples, surface texture, a 3D aspect.  I think of this 2d/3d region as bas-space, a continuum that begins with flat flat 2d. That surface develops 3d qualities with texture, or that favorite detective story clue, the impression emphatic writing makes on the sheet below. Shade over that with a pencil and you can read what the evildoer wrote. 3d emerging from 2d again. Or complicating it.

In reliefs 3d can build incrementally and logically outward from mere etching to low relief to high relief — and now imagine a kind of duct-tape-removal sound as it pops away from its substrate. Sculpture in the round.

Linguistically rich turf. We throw around the terms 2d and 3d as if we knew them, as if we knew the difference between cabbages and plums. But when you think about origami, a rolled newspaper, a once-folded sheet with a minor faint crease — it can be rewarding to ponder the nuances.

And here I stop, a step away from topology, from tesseracts, Klein bottles, Mobius strips. Because to think about these you must plant your feet on very different turf.


All this ensues from my blogpost of February 4, Architectural Message of Chartres Cathedral. Architecture is usually spoken of as a 3D artform, rooms, domes, stairways. Volumes.  But humans are necessarily smaller scale. In order to interact with architecture you must approach it, meander in it, tire of its lengthy halls. Thus the 4th dimension time becomes part of what an architect must design for. You don’t route traffic to the throne room through the scullery.

Likewise grand public architecture taxes the architect with producing the right silhouette.  A fortress from a distance should look grim and intimidating, a palace must show luxe even far off on the horizon. Architects are employed to understand these messages and to deliver them.

Sculpture in the round also has this 4D aspect.  If you see the Nike of Samothrace from the front you may guess the backside but you have to walk around it to be sure the sculptor hasn’t add a tail.

Also last week I also spoke of barn-raising in 1800s America, how it took a community to accomplish the feat.  Then after the work came dancing and feasting, festivities where humans made merry together. And thus wove a deeper community.

Today as you drive across rural America many of these structures are slumped sideways, abandoned. Yet think of the planning and sweat that went into these massive buildings.  Interesting that hardly any houses which would have gone with the barns are seen from the road. Houses are flimsier. They didn’t tap such a widespread community in order to rise. A community now morphed and unrecognizable.



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