This text was originally written in December 1990 as a personal answer to John Osbourn who asked the title question in his private publication "The Amphographer" which I believe originated as a newsletter of the "Escher Special Interest Group" from the American MENSA Society.


During the short time that I received copies of "The Amphographer" it seemed to be primarily a cross between a gallery and an instruction manual for second-rate imitations of the tessellations (i.e. tile figures) from M.C. Escher.

Although the tessellation figures are possibly more interesting than the (probably more popular) "Impossible Perspectives" and are certainly a worthy subject for study I could not avoid a feeling of frustration that there were many important aesthetic and philosophical issues which were directly relevant to both Escher and my own work (as a computer artist) that were not being discussed in "The Amphographer".

The frustrations generated by "The Amphographer" coupled to the frustrations generated by the way the artistic use of the computer was developing at that time (1990) exploded into theoretical speculation when triggered by Osbourns question.

Now (in 1997) after re-reading the text as a result of contact with two young (Dutch) artists I am convinced that many of the issues raised are still valid as inspirational seeds. The text has therefore been edited to distance it slightly from the direct context of "The Amphographer" in order to make it more readable for outsiders. However, without its original context this text would almost certainly never have been written. Hopefully, if the internal structure seems a little illogical, the reader will bear in mind that the original context gave a unique opportunity to connect and contemplate things which would normally escape attention (at least by me).

Unfortunately, after submitting the text I never heard any more from John Osbourn or "The Amphographer".

Finally, I should add that this text is based completely on speculation based on information in "The Amphographer" coupled to the personal experiences generated by my own (visual and theoretical) work. Neither before or after writing the text have I made a special study of Escher. Although I make statements regarding him and his work it should be clearly understood that these are my statements and I have no way of knowing if he would agree, or not!


As with all interesting questions there is probably an abundance of answers to the question "Why is Escher swept under the rug?".

a. Cultural Politics:

One possible answer lies in Cultural politics. From the seventies to the nineties (as long as I have lived in the Netherlands) Dutch cultural tradition has been strongly anti-intellectual. Also the dominant (although fading) cultural tradition of religious apartheid traditionally precludes confrontation with concepts which can be considered subversive of ones own. In addition, the Calvinistic Petit Bourgeoisie appear not to be able to tolerate success in others.

Current cultural politics in the Netherlands are orientated towards promoting Dutch art as the art of the personal anecdote -the visually charming eccentricity. This is also consistent with a society which needs to ritualize human contacts and is incapable of handling true individualism without the safety of rendering it harmless within the category of "ART".

As a formalist, perfectionist and individualist, Escher would clearly be viewed as being more of a threat than an asset by a complacent and autistic society.

b. Art History:

A second possible answer can be found in the context of (Art) History. If one takes an historical view then one is concerned with the contribution from out of the past into the present. The more other artists claim an artist as predecessor and inspirator the greater is their "Historical Value". In this sense, Escher appears to be of little historical value. If he did not sell his work for large sums of money then there are no powerful parties with large vested interests to push him as an historically unique and inimitable genius.

c. Art Theory:

However, perhaps the most interesting range of answers (or questions to be asked which may lead to interesting speculation) can be found within the field of art itself. It may be necessary to ask the question "Was Escher an Artist?", and even to enquire into the nature of art itself. Certainly within the context of the "Amphographer" and its relationship with my own work as a "Computer Artist" I hope to raise some interesting issues. Perhaps one reason (even, in some sense, the final reason) that Escher is swept under the carpet is that, with the exception of certain freaks, people in general have tidy minds and if Escher is not under the carpet then people simply don't know where else he should be put!

The relevant question then appears to be "If Escher should not be under the carpet -then where should he be?". We must create an artistic context (or tradition) within which Escher has a permanent place as inspirator and guide.

Luckily, Escher appears to have an intelligent and loyal son who can correct my hypothesizes, or statements, if I am wrong.


a. A Lack of Dimensions:

During the public meeting to introduce the Dutch society "Ars en Mathesis" the chairman Prof. v.d. Blij, asked the question "What, for a Sculptor, is the relationship between the different profiles of a sculpture?".

Having been trained as a sculptor, I experience this question as being of fundamental importance. My answer is: Contrary to the painter, who reduces everything to a two-dimensional (visual) plane, the sculptor thinks in terms of volume in multi-dimensional (conceptual) space.

For a sculptor the profiles simply don't exist -because although the information is (partly) visually received, the object itself is not a visual object but a conceptual object.

Roughly; the painter looks in two-dimensional space and the sculptor thinks in multi-dimensional space. For the sculptor, a cube does not have six faces but is a point in three-dimensional space while a sphere is a point in infinite-dimensional space. Both cube and sphere have mass (and are material objects) but neither have profiles. That is why a sculptor in the company of painters feels like a cube in Flatland!

b. The Theoretical Space:

The contrast between painter and sculptor is (when projected) of fundamental importance for the perspective within both art and mathematics (and certainly affects our view of their relationship).

The spatial contrast between concept and percept within (so called) visual art has just been suggested. However, regarding mathematics the situation is even more serious because it would seem that for both the amateur and for the draughtsman/painter (i.e. the inhabitants of Flatland) mathematics is synonymous with calculation -while for the multi-dimensional being the relationship between mathematics and linguistics, logic and computer science (as subset or superset) remains more important.

In multi-dimensional space Art, Mathematics and Computer science have the problem of representation as a common point.

The role of the formalization and abstraction process together with an understanding of the topologies and domains of the (perceptual) translation and description spaces -including the relationship between the individual point and the generic space in which it is located, can be found at the intersection of Art, Mathematics and Computer science. Outside this intersection lies only a (not completely uninteresting) projection within a space with a reduced number of dimensions.

Is not both art and mathematics ultimately concerned with the definition, ordering and manipulation of relationships between characteristic identities?

c. A Fear of Heights:

The difference between pure and applied mathematics is the degree to which the (invented or discovered) characteristic identities are bound to specific objects or systems. Mathematics is not pragmatic (the ancient Greeks knew that) -it is the unimaginative pragmatism of some applications (and their practitioners) that are boring and pedestrian!

Living in multi-dimensional spheres, I can promise the inhabitants of Flatland a good argument. But let us not dig defensive trenches for we must keep the fight in the open space. Hopefully, art and mathematics can thus be lifted to a higher dimension. We have only our fear of heights to fear!


* ( Metamethical -started life as a typing error which )
( sounds a bit like "Mathematical" and looks like it )
( might have something to do with 'Meta' and 'Method' )
( or even 'ethics' -however beyond that we do not yet )
( know what it means, so it may be extremely useful! )

A. A Metamethical Premise:

That Art is a Multidimensional Statement in which;
-Translation (multi-dimensional projection)
-Paradoxal ambiguity (multi-dimensional interweaving)
form an essential part of the statement.

B. So Was Escher an Artist?

Perhaps we can examine the work of Escher (and other similar images such as the imitations presented in "The Amphographer") within the context of Metamethics to see if we can gain any insight into the function (and functioning) of art.

A useful starting point may be the question (or set of questions) "Was Escher an artist?" (and its related questions "Am I -or John Osbourn or anyone else, an artist?").

It appears MCE claimed he was not an artist; but in which context must this be interpreted?

i. The Multi-Dimensional Nature of Art:

"Art" has many connotations; as an Object (presented as commercial or cultural artifact), as a Social Ritual (at the gallery during the opening), as an Qualitative Judgement (that's a real work of art), as a Process (either producing an artistic object or as a substitute for it) or even just a Skill (the art of Art).

Certainly my opening remarks about Dutch cultural politics clearly show I do not wish to associate myself with the Dutch social ritual of art, nor presumably do they wish to associate with me. In that sense it is possible that MCE did not wish to be associated with the ritual.

However there may be a deeper reason which is not unrelated to the apparent paradox that he considered the tessellations as his main work and yet apparently presented them rarely in an autonomous artistic context.

ii. Art as (Grammatical) Process:

If the Art Object is considered to be a (visual) statement regarding the artistic process, then the process of art production must be primarily concerned with the generation and manipulation of statements.

So the artistic process is primarily concerned with grammatical processes (including the processing of grammars).

Possibly there are two (distinct?) grammatical processes involved in creativity; on the one hand the experimental generation of new grammar(s) and on the other, the generation of new insights by manipulating existing grammar(s).

These two modi are not easy to combine -it is difficult to explore something and to use it efficiently at the same time. Although of course an attempt to use something is a way of exploring its nature it remains difficult to use something effectively if it is not fully understood.

As a result, in many art forms (including the commonplace example of a good film from a bad book) there appears to be a developmental phase and an expressive phase. The artist (and often the scientist) who has become famous for his sublime invention often appears (on closer inspection) to have achieved fame by perfecting the work of some lesser known colleague(s).

If MCE received the idea for his universally acclaimed "Impossible Perspectives" from the Professors Penrose, then it is not strange that these were successful (the grammars were developed and he merely had to adapt them to his expressive purposes -no mean task, but I am talking functionally and not qualitively). Also, it is logical (and a sign of his quality) that he considered this body of work as not being essential (as essence) to him. Not his best work, but his true work was the development of the tessellation grammars.

iii. Transcending the Grammatical Process:

However a work of art is not purely a grammatical statement. Otherwise every mathematical, logical or linguistic well formed formula (i.e. grammatically correct statement) would be a work of Art.

A (Metamethical) work of art requires Paradoxal Ambiguity within a Multi-dimensional Nexus of Translations.

As an artist with a highly developed sense of craftsmanship (or a craftsman with a highly developed artistic feeling) MCE probably had difficulties in developing his tessellation grammars sufficiently to meet these high standards. Certainly I know from my own work that it may cost several years of playing with ideas before one is able to weave a suitable level of complexity -and then one has made a single work. Other works, when not simple variations or disguised copies, may take then months (or even years) of further study. We know from the letters from George Escher that (before the years of shaped canvases and other avant garde extravagances) CME had problems with reducing an infinite pattern to a finite presentation form.

Presentation problems are a troublesome, although sometimes rewarding, time consuming business. If he felt (and it seems that he did feel) that developing the tessellation grammars was his true work then is it logical that he preferred to spend his time on that problem and not the presentation problem. As a result the emphasis falls on research and not in the production of works of art -and it is logical that MCE is also not arrogant enough to call himself an artist.

The problem is, what does one call an artistic Bhodisvata who concentrates on valuable artistic research without wasting time on (seemingly) unnecessary artistic production. This is still a current problem so long as research grants are required for study of the integration of the computer in artistic production without having to compromise the name of art by pretending that all the results of the necessary investigations are artistic statements.

Also I believe that most of the Escher imitations published in "The Amphographer" and elsewhere suffer from the same problem of being possibly interesting research material but not making valid artistic statements.

C. Towards Defining the Grammatical Nexus:

It has already been stated that a work of art must be a nexus of interwoven grammars.

So what are the grammars (or families of Grammars) that we might expect in the nexus?

I believe that while there is no upward limit, the minimum is at least three (which may also prove to be compound grammars) namely:

A work of art says something about its medium, a work of art says something about its artistic context and a work of art says something about the behavior of our sensorial system.

However an interesting exception to the last (sensory) aspect is literature, which is in fact a mental and not a true sensory art form. Or perhaps it is truer to say that in literature the mind is treated as a sensory organ. True a bibliophile will hire a good typographer, possibly an illustrator and certainly a good bookbinder but perhaps the bibliophile is no real lover of literature. Certainly the writer, unlike other artistic producers has, in general, little interest or say over the presentation form of their work -but literature is surely the exception that proves the rule (although sculpture, as stated earlier is also an interesting border case).

So, with literature forming a possible exception, a work of art should contain the above mentioned three sets of grammars intertwined to form a (possibly inextricable) nexus.

For completeness, we should add that these should be seen as categories (or families) of grammars and that, for example, under the Artistic aspect we should include complex Philosophical and Aesthetic interactions between personal and social, physical and mental, perceptual and conceptual, image and reality based grammars.

i. Concerning The Medial Aspect:

Information regarding his physical medium is at present not readily available to me but the prime conceptual medium for CME was obviously his tessellation grammar (actually I should say grammars -but then I get into grammatical problems with the word 'medium').

These tessellation grammars he (justifiably) assumed were his invention (certainly the specific grammars used to produce his specific images -even if there were a few proto-types before him). Obviously, his works make unique (and valid) statements regarding this (conceptual) medium which is explored and expanded as part of the work process he invented.

ii. Concerning The Artistic Aspect:

Because he used both his physical medium (i.e. printmaking) and his conceptual medium (ie. the tessellations) in an artistic context the collection of works produced by MCE also make artistic statements (at the very least about their uniqueness and their validity within that context).

Because this text is primarily concerned with re-examining and re-defining the Artistic context for MCE we shall need to explore further before making conclusions regarding this aspect.

There remains then the question of the sensory (visual) aspect.

iii. Concerning The Sensory Aspect:
a. Expression or Meaning?

Within a visual context, a line is generally a carrier of expression while a form (figure) is generally a carrier of meaning.

However, a closed line becomes a form (figure) simply by filling in the enclosed area. At that point the line loses its potential for expression while the figure (form) becomes more dominant by separating itself from the background.

Normally the border between figure and background has no expressive quality but in the tesselated figures produced by MCE the borders have a double function within neighboring forms (i.e. the figure of a fish in the foreground may form the legs of a man in the background). This ambiguity demonstrates an isoformity between each figure which visually links figures which may be conceptually unrelated.

I believe, and the visual contributions in "The Amphographer" support this belief, that the formal constraints on the line (requiring it to become an ambiguous boundary between two different figures) make it in fact unsuitable for artistic use and CME was absolutely correct to reject its use except as a technical necessity (i.e. to visually clarify an otherwise unrecognizable form).

b. Form or Line?

As far as I can see, there are two possible solutions to the problem of the line losing its expressive quality due to the constraints of the form:

One solution is to treat the line as a border and accept the loss of expression (as CME in fact did).

This also introduces the not uninteresting problem of the relationship between the visual classification of the form and the topology of the coloration restraints implied by the need for contrasting borders.

The second solution is to reduce the forms to lines (as often happens in Celtic knot patterns but also in the patterns from the Chimu culture which were illustrated in a copy of "The Amphographer").

In both the above mentioned solutions a form of (visual) paradox (a Metamethical condition for art) becomes automatically apparent (namely, either the confusion between foreground figure and background figure, or the confusion between foreground line and background line which is heightened by the ambiguity of a line which is also a form). Within the context of ambiguity, the Celtic and the Chimu patterns may be considered more 'powerful' than those of Escher.

c. Graphs or Glyphs?

The shift from line to border literally makes the forms more 'solid' so that it becomes easier to play with graphic (or visual) rhythms such as reversal of form or direction and color so the potential for visual effect is drastically improved.

Also by visually strengthening the form, the shift from line to border magically produces 'glyphs' (i.e. the independent but interrelated forms that are so important in the work of MCE).

(I must admit I rather like the word glyph, which John Osbourn uses in "The Amphographer" and I certainly prefer it to the term 'icon' which has awful semeiotic connotations with misunderstood notions of language as coded messages.)

So now we can forget the Graphical qualities of MCE and concentrate on his Glyphical qualities.

f. Escher and his Glyphs

The angularity of MCEs Glyphs (i.e their strong formal character) appear to emphasize their 'glyphicalness' (i.e the fact that they are manufactured visual objects and not artificial visual illusions.

Paradoxically, the (visual) vitality of the tessellations emphasize the dynamic quality of life. The abstracted, living creatures which form the glyphs sit exactly on the border between life/freedom and formalism/artificiality/image/art. That is a powerful visual paradox and at the same time a powerful artistic metaphor. Because the patterns sometimes literally break free (even sometimes escaping, momentarily, the flat paper) I cannot believe that this is not a central (intended) theme in MCE's work. This theme is also entirely consistent with (and has been made a fully integrated part of) his medium (i.e. both the physical woodcutting and the visual and conceptual tessellations).

g. The Amphoglypher - A Metamethical Publication?

A transfer of attention from the line to the glyph implies, it would seem, not only a visual improvement. The glyph is more suggestive regarding not only the grammars which generate the form (mathematically and visually) but also the nexus of grammars concerned with the philosophical and artistic interpretation of the glyph (which is generally a carrier of meaning -in contrast with the line which is more a carrier of expression ). One may also assume that the generation and development of a theoretical and practical context for the work of MCE is a better tribute to him, by giving him a functional (art) historical context, than the presentation of (generally) second-rate imitations of his work.


A. Research and Knowledge:

I believe it is not derogatory to state that there is evidence that MCE did not in fact fully know what he was doing.

In fact it is certainly a basic condition of fundamental research (both in science and in art) that when researching the unknown one cannot know what is being investigated until after one has investigated it.

Even today there is still no easily available (art historical) language to describe the work of MCE: So how could he explain himself and how can we discuss his work?

B. Formal Grammars:

Although it may be denigrating (and assumptive) to give a too precise definition of any artist's work, it seems fairly clear that within the context of Western Art History MCE was the first since the (Renaissance) invention of pictorial perspective to research the role of formal (and semi-formal) grammars in the image making process.

This work was done before the early beginnings of computer art where these problems became once again the basis for aesthetic research (although so far as I know this developed independently of the work of Escher -except on the trivial level of stealing his images).

Unfortunately the conceptual basis of computer art seemed to get quickly disrupted by the financial rewards of exploiting glossy simulated photographic realism, graphic user interfaces and standardized image generating and manipulation packages. The computer quickly degenerated from being a formal tool for research into an informal visual toy for consumer amusement. Who is interested in the problem of formulating their thoughts with literary precision when as consumers we can spring from image to image stimulating our senses, if not our minds.

Modern science however, has just begun to get involved in the complexities of grammatical nexi and emergent behavior such as can be found, for example, in the effect on the climate of such seemingly unrelated phenomena as molecular interactions between wind and waves, the destruction of the rain forests and the use of household aerosols.

It is a pity that artists generally seem unprepared to confront themselves with the complexities of grammatical nexi and emergent behavior which can be found in good art.

C. Grammatical Structure as a basis for Art Criticism:

The concept of a nexus of grammatical structures, and the idea that that the "quality" of a work of art is related to the intensity of the (paradoxical but coherent) interweaving of the grammars, should give us a useful tool for a critical analysis of art.

My original (1990) text at this point was concerned with a criticism of some of the works presented in "The Amphographer". Obviously, without the visual evidence of the images concerned the remarks become less valid. However the specific remarks can lead on to more generalized comments which may still be worth making:

i. The Question of Originality:

As stated earlier, creative use of grammatical systems can probably be reduced to one of two strategies -Expression or Invention.

Expression involves using existing grammars to make (new) artistic statements while Invention involves the creation of new grammars by some kind of Meta-Grammatical process.

Superficially, Invention may seem to be of a higher order (more fundamental) than the (more practical) Expression. However, the idea that both processes may simply be the expression of more abstract Meta-Grammars tends to equalize the relative merits of both strategies. An objective evaluation should therefore be based more on how creative was the act of obtaining the Meta-Grammar and less on the domain of strategy (Expression or Invention) in which it was applied.

ii. Artistic Statements:

A careful observer may have noticed that the creation of an 'Artistic Statement' is include in the definition of Expression while it is omitted from Invention.

This suggests that Expression is a more direct strategy than Invention -i.e. Invention may be creative, but is it Art?

Hopefully, a formula for the creation of Art cannot exist (by definition) so Expression must involve some form of creative explorative invention -just as Invention must involve some form of expressive interpretation in order to place it in an artistic context.

Although Art is generally considered to be a creative process, it is a strange paradox that the more (fundamentally) creative strategy of Invention is less likely to produce an "Artistic Statement" than the less fundamental strategy of Expression (i.e. adaption). Also the more original a work is the more difficult it is to understand it and assess its value.

It should also be clearly understood that by 'Expression' is meant Artistic Expression (i.e. the expression of an artistic statement) and not Personal Expression (i.e. the expression of a personal emotion -which is at its lowest level not even creative, let alone acceptable as Art).

iii. The Specific and The General:

Perhaps the artistic process is primarily a dialogue between the Specific and the General: A question of what society does with the artists constructions and how the artist is influenced by the conscious or unconsciously accepted socially constructed conventions. Although somehow the Specific and the General may appear to be opposed to each other (the world inside and the world outside) they are in fact intimately (inter)connected.

If I believe that I have seen a Monster then society could view this as an insignificant personal aberration or it could consider it as vital evidence that such things exist and that there was a serious risk of great dangers looming large.

Obviously the view of society regarding the normality of seeing Monsters can also be of critical importance to how I view myself if I believe I have just seen one.

Of course what I saw may not have been a Monster but that was the nearest (socially provided?) category I could find -what then is the chance of discovering what it was I really saw?

iv. Historical Topology:

If only to avoid mind numbing repetition, it seems reasonable to ask of any work pretending to be of artistic merit: "Which Artistic Statement is being made which has not already been stated in a previous work?".

Personally, I am interested in a less intuitive approach to the generation of a meta-grammar, or calculus, capable of specifying (or even generating) classes of art works distinguishable in terms of their relevant characteristics.

Another potentially interesting question which comes to mind is: "Are there transformation rules which fundamentally change the characteristics of the underlying structure?" (i.e. What is the relationship between the different structural levels -in an Escher tessellation, but also in any art work?).

For example, viewing the underlying structure and its subsequent transformation within a tessellation as separate levels suggests the possibility of local modulation of the (glyphic) form. In fact MCE has already done this in "Liberation" (fig. 13 in 'Godel, Escher, Bach') and "Mosaic II" (fig 14 in GEB) but in the first example the sequentiality of the transformation rather suggests a unique event and the gay abandon with which the transformations are applied in the second example is so masterly that one tends not to notice what has been done. Certainly there would appear to be room for work playing with the visual equivalent of the "Philosophers Stone" weaving transmutational rhythms before our very eyes (to say nothing of the implications of re-evaluating the weaving of textiles as a mental and not a physical process).

Strange that it seems of art historical importance who "invented" cubism, and yet probably very few people know (or care) when a specific computerized image processing technique was introduced or who invented it.

v. Paradox and Aesthetics:

In the original text the role of paradox was rather heavily emphasized. I now think this should be replaced by the concept of Aesthetics, which I consider to be concerned with establishing and maintaining equilibrium within a dialectical (i.e. contradictory) nexus of rules, desires and possibilities.

In another (later) text exploring the concept of Aesthetics I came to the conclusion that 'Paradox' is an unavoidable consequence of the Aesthetic process being placed within the context of western (male) philosophy and that it is not essential to Aesthetics. In 1990 I had not realized how culturally dependant a fascination with paradox probably is. Nevertheless I am still culturally conditioned enough to be rather fond of the paradoxical nature of paradox!

vi. A General Impression:

My knowledge of the underlying tessellation grammars was insufficient to judge how technically creative the works presented in "The Amphographer" were.

Often they were visually weak (due to poor reproduction?) and in general did not seem to be making powerful artistic statements.

Obviously some images were better than others and it will probably not surprise the reader to learn that the more coherently complex (and preferably paradoxical) the interweaving of the different (visual, interpretational, structural, etc.) grammars became the more satisfying I found the work.

vii. Free and Bound Interpretations

One of the techniques described by John Osbourn in "The Amphographer" is a free associative interpretation of the form(s) being created so that the tessellation can be developed further in terms of recognizable figures (i.e. fishes, birds, father christmas or whatever). In reference to the famous psychological ("ink-blob") tests John calls this associative process "Rorschacking".

Perhaps all interpretations can be dismissed as "high level Rorschacking".

Apparently, George Escher stated that his father could get quite irritated by reactions based more on the imagination of the viewer than the intention of the artist and it is indeed irritating when people insist that one has made statements which one has in fact not made.

I am also not someone that believes the viewer is free to indulge in mental masturbatory rorschacking over every art work which takes his or her fancy. I do believe it is the task of the artist to make his/her levels of meaning (grammatical nexus) so rich and coherent possible, and the task of the viewer is to respect this coherency. However, just so as a mathematical formula can be valid in contexts which the author had never imagined -so, can an art work function as a model for situations which lie outside the the intention (or even experience) of the artist.

Possibly it is even the function of an art work to act as a formal system which can be a model for unspecified but topologically equivalent contexts -rather as Jung suggests in his introduction to the Wilhelm translation of the I Ching.

I am sure MCE enjoyed exploring his garden of marvelous richness and that he did not spoil it by going around planting his favourite flowers everywhere just to express himself.


A. Looking for Movement:

Considering the fact that Escher does not easily fit into the current art historical context it would seem necessary to invent one for him. In effect this would amount to an historical fraud unless we approach it in the spirit of exploring the potential characteristics of a, now barely visible, possible future artistic movement.

B. Art Forms, Genres and Movements:

In "The Amphographer" John Osbourn has asked: "Can tessellation be a specialized art form". This would obviously be advantageous because it would give him the freedom to define his own criteria independent of those of other art forms (an ideal situation for any artist, but rather difficult for the museum directors, the critics and the givers of grants).

So perhaps we are lucky that not everything in life that is desirable is also feasible. Let us pose a parallel question: "Can computer art be a specialized art form?". In order to answer this and the original question we may possibly need to ask a third question, namely: "What is an Art Form?".

i. Form and Space

Dance, theatre, music, opera, visual arts (and sculpture?) are different art forms and within these we find different artistic sub-forms. In music, instrumental: symphonic, chamber, and solo or vocal: choral, group and solo. In the visual arts, Photography, painting (water color and oils), drawing, printmaking, film, video and computer art sub-forms.

The different sub-forms are difficult to relate to each other when crossing sensory boundaries. How can one relate printmaking to chamber music?

In music scale and sound production appear to define the boundaries while in the visual arts the function of time and the means of image production appear to form the bounding characteristics.

Historically the boundaries are probably purely pragmatic -a painter and a printmaker have practically no common tools (even paint and ink appear to deny their common origins due to the way they need to be modified to suit the demands of the different techniques).

Nevertheless, theoretically seen, the media do define their own characteristic parametrial spaces so that a classification could take place on the basis of the number and type of parameters involved, for example; time, physical space, sound, light modulation or emission, individuality (uniqueness) or repetition, plus the human, mechanical or electronic methodology of production and processing of signs and signals.

Clearly, characteristic variation in the construction of the parametrial space could have implications for the topology of the space, which in turn would lead to a different set of problems involved in the manipulation of each specific space or medium (i.e. changes in the geometry of the grammars). It seems therefore not unreasonable to bind the concept of "Art Form" to the characteristics of the parametrial space, or medium, involved.

Tessellation Art is then not an art form, because it is not in conflict with the traditional media, however Computer Art (if it exists) may be considered an art form purely on the grounds of its instrumentarium. The ease with which digital data can be translated into sensory information also implies that the previous correlation between art form (medium) and sensory information channel is no longer valid in relation to Computer Art. Possibly, because of the fundamental (i.e. topological) differences between Art Forms, a tessellation in a traditional medium may have other implications than a computer produced tessellation.

ii. Genre and Space

A genre, for example, still life, landscape, portrait, historical or religious work is generally concerned with subject matter. Because a photographic landscape has different connotations for me than one in oils or water color, I am tempted to say that a "Genre" is concerned with subject matter within a medium although there may be parallel genres within different media.

Tessellation appears therefore to be a genre.

iii. Movement and Space:

A movement, for example, Baroque, Rococo, Art Nouveau, De Stijl or Pop Art is concerned with paradigm shifts which may cut across the boundaries of art forms or sub-forms, so that several art forms may participate in the same movement as the paradigm shifts are tested in the different medial spaces.

If Computer Art or Tessellation Art are able to contribute towards paradigm shifts across the Art Form boundary, then they may be considered to be part of a Movement.

C. Looking for New Movements:

It is no great compliment to Escher to consider him as the solitary exponent of an obscure genre (or even two obscure genres) of printmaking, which is probably the official art historical view. It is a far greater compliment to expound him as the forefather of a new movement.

i. Post Modernism and the Medium:
a. Post-post

Economically we seem to be in the post-industrial period. Culturally we seem to be in the post-modern period. Firstly, these rather negative labels are not very useful (because we know what has gone but not what remains or is coming) and secondly, we may assume that there is some connection between the two periods which are parallel in time in two different domains.

The post-industrial period seems to focus around the service, computer and the media industries (or probably, servicing the media industry). I say "media" and not "information" industry because information is dependant on context and post-modernism has destroyed context to the extent that (outside specific commercial or scientific applications) the cultural concept of "information" died with the decline of the printed word (see the books of M. McLuhan -for those that can still read).

Post-modernism is beyond ideology and cultural aesthetics,instead of actively participating in an ideology or cultural aesthetic, the historical sequence is presented (as in a computer program menu) so that the player may freely select (without real commitment) their personal mixture of the (constantly rewarmed) cultural soup without ever actually getting around to eating it. By reducing culture to a simple (a priori) menu selection, post-modernism destroys the concept of the future by denying the concept of cultural progress.

Perhaps the automated synthesis of physical (and cultural) products will also eventually destroy the concept of economics by destroying the concept of human labor as an economic principle. The post-modern media are self-referencing and auto-destructive.

b. Social Meta-systems

Scientifically, we are now in the age of the computer simulation. If one can't make a computer simulation of a specified phenomena then one cannot claim to understand it. Also computer simulations are increasingly used to replace expensive and troublesome practical experiment. Practical experiment becomes less a way of gaining direct knowledge and is becoming more a way of testing the simulation so that the simulation and not the reality become the new medium for practical experiment. Through this shift towards gaining knowledge more by manipulation of the simulation than by the manipulation of reality, Science moves toward Art.

Unfortunately, Art has not realized this and so can draw no useful conclusions.

Culturally, economically and scientifically we have moved beyond the world of objects and have entered a universe of abstract meta-systems.

By doing so we have increased our practical control over the world of objects, but this raises the question: Have we also increased our level of theoretical understanding which will allow us to exercise our control with wisdom?

c. Social Schizophrenia

The economic and cultural meta-systems seem to have at present almost no function other than their own self-perpetuation. Historically, by determining aims and dispensing cultural status, the aesthetics (and ethics) of cultural philosophies created powerful channels for the (re)distribution of wealth which sustained the operations of economic systems .

Of course economic currents were also powerful modifiers of cultural values, so both systems were linked.

A severing of the link because the two systems have become too self-referencial could damage the balance of power and destroy both systems if they cannot survive independently. If they remain linked, then the collapse of one may lead to the collapse of the other.

The scientific meta-system (as long as the economic system still functions) is also extremely useful in developing wealth generating technologies.

Nevertheless, the relationship between culture, economics and science demonstrates a strange social schizophrenia. While culture and economy seem to be getting more autonomous (as a result of the collapse of the ideological/political interface) science seems to be in danger of loosing its traditional autonomy, so the chance of a fundamental 'second opinion' may be getting less -especially if artists also let themselves get seduced by current cultural trends.

A second interesting set of contrasting social forces can be seen in the fact that the collapse of ideology has reduced the level of social discussion and control in economic and cultural systems so that the understanding within the culture of the subtle interactions within and between these systems has become almost extinct, while at the same time the scientific community is at present developing more and more interest in the interactions and translations between sub-systems which were previously considered to be unrelated but are now seen as part of a single grammatical nexus.

Culture is falling apart and science is coming together.

d. Social Chaos or Social Ecology?

Is our social structure going to disintegrate into an anarchistic chaos of autonomous (and mutually destructive) systems? Will it collapse due to its own lack of creative regeneration -a victim of its own tautology or will it develop into a finely balanced ecology of symbiotic sub-systems?

ii. Escher, Pop and the Meta-jump

It would seem that the shift from object to meta-system presents us with many problems and responsibilities for which we have too little experience and knowledge to be able to cope with properly. The ghosts of Icarus and Prometheus seem very present.

Perhaps if we could understand how this shift took place we would be able to find ways of playing with the problems and understanding them better.

a. Warhols World

One Art Historical way of jumping from object to meta-level was via the Pop Art.

By taking popular culture as a subject matter for art and (thus) at the same time becoming part of that culture, Pop Artists closed the loop on themselves and shot through to the meta-level.

Interesting is the fact that Andy Warhol seems to have operated on the object level in his screenprints and on the meta-level in his books. After Warhol the road was clear for other post-modern artists to move in and exploit the system on the road to fame and glory.

The problem with this route is that it is largely intuitive and although it may be a nice game to play it probably generates little concrete knowledge relevant to a solution of the problems which it creates.

b. Eschers Universe

Any formal system which is interpreted becomes a meta-language for the world in which it is interpreted. Representational Tessellations can be considered to be interpreted formal systems which therefore automatically introduce the phenomenon of object and meta-level. So Escher is the other, Art Historically earlier, way of jumping to the meta-level.

The advantage of this route is that it uses formal systems, so it already includes in itself the tools to objectively investigate the problems which it creates. Unfortunately, because formal systems are fairly alien to the modern art tradition (which is practically an escape from formal restrictions) few artists have chosen to seriously investigate this approach.

D. Finding the New Movement:

i. Post-renaissance and Pre-post-modern

One of my personally most astounding discoveries regarding Escher was the discovery that for a part of my life he was a contemporary artist.

From his imagery, I would have placed him as a contemporary of Durer. His spatial loops could have been part of a Renaissance experiment with perspective, although his representational tessellations seem to play with and then eventually reject Renaissance pictorial space.

However, by introducing the meta-loop without pushing it to its post-modern limits he appears to be a pre-post-modern artist. By a series of (almost surrealistic) time shifts his use of formal systems would seem to create a conceptual continuity from the problems of Renaissance pictorial space to the solutions of Post-Post-Modern meta-space.

Once this continuity becomes visible it is not MCE who has a dubious claim to art historical importance -to the contrary, almost all western art since the renaissance would seem to be largely irrelevant (or at best a proof of its own erroneous deviation).

ii. Formalism and Free Will

Modern art, from the impressionists onwards, is largely (outside the constructivist tradition) an escape from formalism and convention, becoming more and more a triumph of the free will of the artist in an expression of their personal ego. The Avant Garde developed new personal languages outside the existing social grammatical nexus and blamed the public for not understanding the new languages. Their own egos, and the commercial exploitation of their work, prevented these artists from realizing that in fact they had little understanding of art in particular or language systems in general. It was exactly this lack of understanding, by both artist and public, which made it so easy for both to be exploited by unscrupulous "Art" dealers. Perhaps, in this perspective the role of Escher as craftsman is important, for the ego based expression of the romantic art tradition causes (possibly for the first time in history) a schism between the anarchistic artist (now bound by their ego) and the craftsman still bound by the demands for (material) quality inherent in the craft (and earlier art) tradition.

Politically, the trend is similar. The destruction of powerful ruling dynasties plus the rise and fall of the dictatorships (the ultimate paradoxal manifestation of free will) demonstrate the spread of democratic expression of free will in recent history. Unfortunately, the complexities of the problems generated by the increased social and material freedom (arising from technological developments) already suggest that there may be limits to the universal expression of free will.

The rise of economic freedom based on uncontrolled market forces also demonstrates that its short-term efficiencies can cause potentially dangerous long-term deficiencies in essential social infrastructures such as health, education, transport and environment.

The renaissance concept of Humanism with its implied emphasis on human free will may well prove to be fatal if humanity does not learn to integrate itself within the context of a restraining nexus of social, material and philosophical grammatical structures.

iii. Simulation and Interpreted Formal Systems/Grammars:

Simulation systems, even childrens games such as cowboys and indians, imply some level of formalism even if only on the level of definition of the components and their general behavior. Without a level of formalism a simulation could hardly claim to be similar to that which it simulates.

Probably as an aid to memory, art in non-literary societies tends to be based on formal rules of composition, proportion and subject matter. These formal rules are often extremely stable over long periods (certainly in relationship to our world of quickly changing fashions). This stability aids recognition within a culture and provides the social continuity which forms the basis for defining that specific culture (and often the political justification for the rulers supremacy). Without cultural, and linguistic, continuity there is no culture and no means to transmit social knowledge across temporal or spatial barriers. We should not let modern art history fool us into thinking that formal systems are fundamentally opposed to artistic systems.

Certainly, simulation systems are invaluable in safely exploring dangerous circumstances, learning basic skills or demonstrating to others the results of certain actions. Traditional art forms generally seem to have their roots in magical rituals where natural and cultural structures are made explicit in order to preserve them directly by literal re-enactment or by transmitting knowledge about them through direct participatory experience. Artistic statements are therefore simulatory meta-statements regarding the universe of the people making them.

iv. Simulation and Medium

Obviously the topology of the medium has influence on the characteristics of the simulation and its relationship to that which it simulates. Representation of time or movement is, for example, easier to express through a dancer or actor than on a single sheet of paper or in stone.

Possibly there was originally also some relationship between the formal demands of early art forms (in terms of repetition, rhyme, meter or color mixtures) and the world view of their users. However it is difficult to see that the Homeric rules of poetry are responsible for the behavior of the Cyclops or even Ulysses. Presumably, the behavior of the characters are derived from other (cultural) grammars than those in which these behaviors (and their results) are portrayed.

Art may be considered as a semi-formal simulatory system, but it would appear that there are higher levels of formalism required if not only the external form of the system is to be formalized but also the internal rules concerning the behavior of the elements within the simulation.

a. Pattern Art

One can suspect that there is a relationship between the use of rules and the generation of pattern. Also, vice versa, the search for pattern implies the search for underlying rules (or grammars).

Recent scientific research into cell automata and emergent behavior has shown (presumably what artists have long known) that there is no direct relationship between the complexity of the rule system and the complexity of the pattern it generates. Simple rules may generate complex patterns and complex rules may generate simply chaos.

In fairly recent art history, the constructivists have experimented with the use of formal grammars (i.e. systems) to generate visual structures and images. Because the general art historical context demanded an emphasis on the individuals unique contribution to a supposed cultural progress the constructivist tradition quickly forgot the anti-ego implications of its own techniques and rather neglected its true historical perspective. If it had been a little more consequent it would have emphasized its relationship not only with late industrial production processes but also with Indian Ragas, Indonesian Gamalan music, the Cabala, Mandala's, Celtic knots, Byzantine, Arabic and other pattern systems.

In other words, Constructivism failed to develop a living tradition by not investigating a whole universe of what may be termed "Pattern Art" which may be principally classified as the use of interpreted formal systems within an artistic context.

Despite Mondriaan, who started life as a "Symbolist", the Constructivists did not generally interpret their structures beyond (early) socialist democratic ideals so it would be incorrect to include the representational tessellations of Escher in the Constructivist tradition. However, I believe it would be correct to place his interpreted formal systems within the more universal context of "Pattern Art".

b. Computer Art

If "Pattern Art" can be considered as a traditional manifestation of a higher level of formalism than the generally accepted aesthetic rule systems which usually generate patterns between cultural objects as opposed to patterns within the object, then computer art (where the formal grammars are implemented by a machine) must represent an even higher level of formalism.

If formalism has a justifiable role in art, then one may suspect that the computer is the ideal means of exploring this role, and the computer is therefore easily justified as an artistic medium.

In fact, the role of formalism in the arts is at present so poorly understood that neither public or artists are generally capable of considering the computer as an artistic medium unless it simulates renaissance pictorial space or it has been de-formalized by commercial "user friendly" interfaces (i.e. instead of being a powerful medium it is reduced to being a simple tool).

This is a great pity, because I believe that ritualization (i.e. formalization) of our cultural, social and natural experiences permit us to investigate the human condition by externalizing it in a multi-dimensional nexus of grammars. Only when these grammars have been made explicit are we free to explore them, their consequences and their alternatives. By presenting the results of our explorations in terms of sensory experiences we are able to transmit cultural knowledge through time and space.

If we do not quickly learn to retrieve, expand and disseminate our cultural knowledge (and intelligence) we may be incapable of surviving in the cultural environment that we have created.

We too may become one of the many creatures who became extinct because they could not adapt to the changes occurring in their environment!


I would not dream of suggesting that Escher, even in his wildest nightmares, considered himself as the new Cultural Messiah.

In fact I believe he (and many others) had (and have) great difficulty in placing his work in a general art historical context.

What I have tried to do, is to show that this context does exist even if, for a number of historical reasons, it has become almost invisible in contemporary art. I have also tried to demonstrate that it was not the fault of MCE, but of other (earlier, contemporary and later) artists that this tradition is still almost invisible despite his revival of it. In addition, I suggest that the continuation of this tradition is probably more important than even MCE might have realized.

Certainly, I do not consider it other than a tribute to his strength of character and artistic integrity that he was able to continue work on interpreted formal grammars and make artistic statements regarding the interaction between reality and simulation within a historical context which might not become visible to others even in retrospect.

I do not believe it unreasonable to claim Escher as the Patron Saint of Transmediaglyphic (metamethical) Art!

Finally, one may seriously suspect that if M.C. Escher was not cleanly swept away under the carpet then the last few hundred years of western Art History would need to be completely rewritten. His position in art history demonstrates the traditional social sacrifice of one person in order to preserve the comfort of many!

Trevor Batten
Amsterdam December 1990/March 1997
 For Rob, Audry and Pieter

html version Sept 2004

A few possibly interesting links:
(added Nov.18 2007)

The Mathematical Art of M.C. Escher

Artful Mathematics: The Heritage of M. C. Escher

M.C. Escher: More Mathematics Than Meets the Eye

Gödel, Escher, Bach

Pattern Syllabus Spring 1996

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