Press and Arts have come to the habit of  making easy money of subjects like the "fourth dimension". So that it is clear to anyone and admitted once for all that the world "has" three or four dimensions and not more, ; time being strangely enough the latter to be taken into account, as if one had had to wait until the twentieth century to admit that time could be of some interest in the description of the world.   

Quite curiously, in spite recent years´ developments around the concept of fractal objects introduced by Benoit Mandelbrot, and despite the remarkable popularity of fractals, the idea of objects the number of dimensions of which is not necessarily an integer, does not seem yet to be a success equivalent to the "fourth dimension".  

The approach used by Duchamp in "The Nine Shots" shows that around 1920, he was quite aware of what part of convention the concept of dimension is actually built on.  

As he was interested in showing one of the possible dimensions that people ordinarily do not think of, Duchamp came to the point of painting with a gun. One must admit that one day or another, this sort of thing becomes quite tempting when dealing with glass.  
Arturo Schwarz describes how it happened in the following way:  

"This area, called "The Nine Shots" is pierced with nine holes. Duchamp's notes 83, 84 and 85 provide more explanations. In order to implement the ideas included in these notes, Duchamp took "a match with a little bit of fresh color on the point of it" and aimed towards a "target" with a "child gun" ("the worse the instrument, the better you measure the skill") from three different points. This operation was repeated "nine times - three times by three times from the same point". With each impact, the matches left a little touch of painting, and in these nine points, a hole was drilled in the Glass. "The resulting figure will be the projection (according to the skill) of the main points of a three dimensional body. With a maximum of skill, this projection would be reduced to one point - the target. With an ordinary skill, this projection will be a gearing down of the target. (Each one of the new points - images of the target - will have a distance measurement. This distance measurement is nothing more than a memory, and may be noted conventionally...). In general, the resulting figure is the visible flattening (captured in action) of the geared down body" whereas " the target is an equivalent of the "vanishing point" (in perspective)"". [1]   

Duchamp's goal clearly appears to be to introduce and represent an additional dimension - here, skill - as well as to explore the associated perspective related concepts. What Duchamp hence makes clear, is that the concept of dimension is all but ontological. That it is only one of the elements of a metaphor, of a model.  

By selecting an aspect of the world which is not covered by Physics, - and it is interesting to note that there is still no satisfactory explanation of skill in Physics - Duchamp makes obvious that the building of a model together with the selection of its associated components are constrained by the aspect of the world that one decides to consider..  

The fact that Duchamp was fully aware of what he was doing when making this choice, is demonstrated by this quotation concerning the definition he once proposed of the "infra-thin" :   
"I selected on purpose the word thin, which is a human and affective word, and not a precise laboratory measurement. The noise or the music made by a pair of ribbed velvet trousers, like this one, when it is moved, is related to the concept of infra thin. The hollow in the paper between the recto and the verso of a thin leaflet... To be studied !... This is a category of which I have been occupied a lot during the last ten years. I believe that through the infra-thin, it is possible to go from the second to the third dimension" [2]   

But one might just as well give as a prototype for these considerations the sort of strange mixture of qualities which haunts titles like "Deux nus: un fort et un vite, 1912" and "Le Roi et la Reine traversés par des nus vites, 1912"   

So, quite logically, if skill is chosen as the topic of a study, one may be led to introduce an additional dimension for this specific purpose, since the concept of dimension is after all nothing else than the representation of a measure. But the introduction of an additional dimension may then result in a modification of the representation and perception of usual objects and the world itself.    

The choice of skill as an additional dimension, and of the context of cannon shooting more specifically, is by no means arbitrary, but educational. It tends to show that the introduction of a concept like the concept of dimension is the result of a project, or better said, of a sighting.   

What is hence - not represented, but - pointed out, is no longer some sort of "funny Physics" it is not even "A world that could be made possible by loosening a bit the laws of Physics" anymore. What is stated aloud, what may be fingered on the Large Glass, is that the characteristics on which our vision is based, might well prove to rely upon quite arbitrary foundations.   

So the remark made by Lebel concerning the "Stoppages-Etalons" applies just as well to "The Nine Shots":    
"Duchamp gives us some hints about his intentions, because, here again, under the semblance of a difficult undertaking, something like an offensive against the logical reality takes form. Duchamp's attitude is always characterized by the refusal to submit to the principles of common realism, and if this refusal is expressed by means of  a sort of mockery, the revolt in it is hereby only strengthened, because it draws along, together with itself, into the incertitude of ridicule truths that were yet impossible to criticize without being considered as mad. Duchamp's method under its apparent flightiness proves to be subtly machiavelic. By opposing humour tainted laws to the so-said serious laws, he casts a doubt on the absolute validity of the latter ones. He gently pushes them towards the approximative, where they build up a system, the architecture of which may clearly appear to anyone." [3]    

In a this, lies the strength as well as the cunning and also the delusion of the visual. And if it may well be - as Hegel notes - that the this gets stale, but it is part of the splendour of the visual to freeze it, that is to say to allow the action of pointing it out again and again, almost at will. But only almost, however, because this movement of "pointing it out again and again" also ends up getting stale.  
 

...the Bride's domain... 
i.e. the upper part of the Large Glass 

...decide to consider... 
It is easy to see how well this idea fits with the Ready-Made concept, which is also - litterally - nothing else than a decision. 

...to go from the second to the third dimension... 
Maybe is it not totally stupid to dream that it might be possible to build a graduated sequence of fractal objects that would allow a "smooth" passage from a 3 dimensional space to a 2 dimensional space. 

... pointed out... 
Just as the Zen satori may be fingered but may not be represented, there is a power in action which transcends the power of language.  

...delusion... 
And of this sort of delusion, this century, more than any of previous ones, will have given amazing examples. 

[1] - A.S & M.D. in "La mariée mise à nu chez Marcel Duchamp même" - Arturo Schwarz  - P152 (1) 

[2] - M.D. quoted by Denis de Rougement in "La mariée mise à nu chez Marcel Duchamp même" - Arturo Schwarz Page 245 Note 10 
  
[3] - A.S. in "La mariée mise à nu chez Marcel Duchamp même" - Arturo Schwarz  P159-160