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# Stott's Theorem of The Pictorial Condition

'Stott's Theorem of The Pictorial Condition' is a pictorial theory developed by Peter Stott (born Burnley, England 1962) from his article 'Transcendental Imaging and Augmented reality', an academic paper published in a journal of speculative research entitled Technoetic Arts ([1]</ref>). This was based on a theoretical model of picturing described in a patent application for an artificial imagination registered at the UK Patent Office in 2006 and published in 2007 and later included in Hans Ulrich Obrist and e-flux's 'Agency of Unrealized Projects'(see link).

The phrase 'transcendental imaging' refers to an initial description of the pictorial condition and its matrix based on the rules of perspective where he states that 'a square has the capacity to be represent a 3D object via isomorphic projection', the transcendental aspect being all the possible form representations outside of ordinary cognitive access. The article expands that basic pictorial geometric fact in terms of how it might be applied to the whole of image culture where the base condition is the 2D data field subject to the geometric rules of perspective.

In December 2018 the artist further clarified his theory of 'transcendental imaging' as 'Stott's Theorem of The Pictorial Condition':

This was amended on 25.04.2020 to include rules 3 and 4.

Rule 1

Via perspective geometry and isomorphic projection a 2D data field made up of one or more 2D shapes may represent (portray) architectonic form whether depictions of real or imaginary 3D objects where a single 2D shape or a conglomerate of 2D shapes may depict a single object or a detail of a single object or a number of objects or a detail of a number of objects and that any isomorphic projection from any 2D shape in a 2D data field may entirely share or not share or share intermittent spatial coordinates isomorphic edgewise with an isomorphic projection from an adjacent 2D shape and that said rules may be applied in whatever combination to any 2D data field and that any inference of spatial orientation that may facilitate isomorphic representations beyond an apparent Cartesian extrusion of forwards or backwards is here categorized as pictorial only and not proof of any actual existence of anything beyond three dimensions.

Rule 2

A 2D data field made up of one or more 2D shapes may be the case or via or not via perspective geometry and isomorphic projection a 2D data field made up of one or more 2D shapes may represent (portray) signs that convey instruction or information whether depictions of real or imaginary 2D or 3D signs where a single 2D shape or a conglomerate of 2D shapes may depict a single sign or a detail of a single sign or a number of signs or a detail of a number of signs and that any isomorphic projection from any 2D shape in a 2D data field may entirely share or not share or share intermittent spatial coordinates isomorphic edgewise with an isomorphic projection from an adjacent 2D shape or any 2D shape in a 2D data field not fulfilling an isomorphic pictorial function may not share or share intermittent spatial coordinates edgewise with an isomorphic projection from an adjacent 2D shape or any 2D shape in a 2D data field not fulfilling an isomorphic pictorial function may share spatial coordinates edgewise with an adjacent 2D shape that is also not fulfilling an isomorphic pictorial function and that said rules may be applied in whatever combination to any 2D data field and that any 2D data field made up of one or more 2D shapes may be subject to Rule 1 and Rule 2 and Rule 3 and Rule 4 together.

Rule 3

Any 2D shape in a 2D data field made up of one or more 2D shapes may represent (portray) a surface that is either planar or convex or concave or planar and convex or planar and concave or convex and concave or planar convex and concave and that said represented surface may be transparent or opaque or translucent or any combination of these surface attributes across its pictorial expanse.

Rule 4

Any 2D shape in a 2D data field made up of one or more 2D shapes may represent blank Cartesian pictorial space but only if all adjacent 2D shapes are fulfilling a pictorial function of sign or form representation or if the case of any adjacent 2D shape is their only pictorial condition.

Some of the points in the above statement are explained in both the article 'Transcendental Imaging and Augmented Reality' (see reference and link) and also the theoretical model of an artificial imagination. (see link)

## References

1. ‘Transcendental Imaging and Augmented Reality’, Technoetic Arts: A Journal of Speculative Research 9:1, pp. 49-64, doi: 10.1386/tear.9.1.49_1