Performing Arts Analogies

Of interest in parquet deformation is the frequent use of performing art terms, such as music (especially so), dance, poetry and theatre (and derivatives), with analogies thereof, used primarily by William Huff, Douglas Hofstadter, and occasional others in their various writings. However, the references are not evenly balanced; by far the most popular analogy made is with music, with the others paling in comparison. Even so, I have decided to include all under a dedicated ‘performing arts’ section as a dedicated subpage. Note that this is a broad rehash of previous writing on music analogies (but not on dance, poetry and theatre). Previously, the music discussion here was placed as a distinct essay in its own right as a dedicated generic parquet deformation (intended as ‘mini essays’ that do not justify a disct page) essay page as Essay 10: ‘William Huff and Parquet Deformation Music Analogies’. As such, although all well and good, I now (30 August 2021) consider that this piece could be improved by extending the remit to include all the (four) performing arts, as above, albeit admittedly with a degree of reservation as to what is such minor inclusions justifying their inclusion.

Each distinct performing art has its own section below, to which I have highlighted in any one section the term in the main body of text for ease of finding, with all the references en masse at the end of each section. Possibly, there may be more discussions, but that shown does indeed cover the main findings. Any (inadvertent) omissions must be of a minor nature, and would not materially affect the piece. The text length shown, typically using existing text from articles, generally varies according to ease of accessibility; sometimes it was possible to copy from a PDF, and others not. To type out in full where otherwise is judged not a productive use of time. Instead, I show excerpts in such cases. Finally, at the end of the piece I conclude my investigation.

1. Music/Composer (8 distinct authors, 40 mentions)

1. William S. Huff. ‘The Parquet Deformation The Mirror-Rotation Symmetry’, 1979.

As such, it is unclear as to quite what this single page document is. From its style and appearance, it appears to be a class guideline. There are two mentions of music analogies.

...These continuous deformations are most often developed along syngenometric lines. The total compositions are not intended to be viewed spatially, but temporally, as a sort of visual music. The Oriental scroll paintings are one of the great few temporal, visual compositions. Viewing them, then, is akin to the manner in which film is seen, poetry read, and music heard.

Also see Huff’s later (1990) ‘Students' work from the Basic Design Studios of William S. Huff’, where the same broad text is recycled.

2. Douglas R. Hofstadter. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20

Simply stated, required reading, with no less than twenty-five mentions of music analogies! Of note (ahem!) here is the sheer extent and depth of the music references. To better understand the context, I have largely included the surrounding text, despite this thus resulting in a somewhat lengthy document. However, without it, the story would only have been partial, and so I have judged a more thorough treatment is in order in this instance.

P. 14. What is the difference between music and visual art? If someone asked me this question; I would have no hesitation in responding. To me the major difference is temporality. Works of music intrinsically involve time; works of visual art do not. More precisely, pieces of music consist of sounds' intended to be played and heard in a specific order and at a specific speed. Music is therefore fundamentally one dimensional; it is tied to the rhythms of our existence. Works of visual art, in contrast, are generally two- or three-dimensional. Paintings and sculpture seldom have any intrinsic "scanning order" built into them that the eye must follow. Mobiles and other pieces of kinetic art may change over time, but often without any specific initial state or final state or intermediate states. You are free to come and go as you please. There are, of course, exceptions to this generalization. European art has grand friezes and historic cycloramas, and Oriental art has intricate pastoral scrolls up to hundreds of feet long. These types of visual art impose·a temporal order and speed on the scanning eye. There is a starting point and a final point. Usually, as in stories, these points represent states of relative calm, particularly at the end. In between, various types of tension are built up and resolved in an idiosyncratic but pleasing visual rhythm. The calmer end states are usually orderly and visually simple, whereas the tenser intermediate states are usually more chaotic and visually confusing. If you replace "visual" by "aural," virtually the same can be said of music. I have been fascinated for many years by the idea of trying to capture the essence of the musical experience in visual form. I have my own ideas about how this can be done; in fact, I spent several years working out a form of visual music. By no means, however, do I think there is a unique or best way to carry out this task of "translation," and indeed I have often wondered how others might attempt to do it. I have seen a few such attempts, but most of them struck me as being unsuccessful. One striking counterexample is the set of "parquet deformations" meta-composed by William S. Huff, professor of architectural design at the State University of New York at Buffalo….

I say "meta-composed" for good reason. Huff himself has never executed a single parquet deformation. He has elicited hundreds of them, however, from his students, and in so doing he has brought this form of art to a high degree of refinement. He might be likened to the conductor of a fine orchestra. Although the conductor makes no sound in the course of a performance, we give much credit to the person doing the job for the quality of the sound. We can only guess at how much preparation and coaching went into the performance.

P. 15. Whereas Escher's tessellations are almost always based on animal forms, Huff decided to limit his scope to purely geometric forms. In a way that is like a decision by a composer to follow austere musical patterns and to totally eschew anything that might conjure up a "program" (that is, some kind of image or story behind the sounds). An effect of this decision is that the beauty and visual interest must come entirely from the complexity and subtlety of the interplay of abstract forms. There is nothing to "charm" the eye, as there is with pictures of animals. There is only the unembellished perceptual experience. Because of the linearity of this form of art, Huff has likened it to visual music. He writes: "Although I am spectacularly ignorant of music, tone-deaf and hated those piano lessons (yet can be enthralled by Bach, Vivaldi or Debussy), I have the students 'read' their designs as I suppose a musician might scan a work: the themes, the events, the intervals, the number of steps from one event to another, the rhythms, the repetitions (which can be destructive, if not totally controlled, as well as reinforcing). These are principally temporal, not spatial, compositions (although all predominantly temporal compositions have, of necessity, an element of the spatial and vice versa e.g., the single-frame picture is the basic element of the moving picture)."

P. 17. This piece also illustrates yet another way parquet deformations resemble music. A unit cell-or rather, a vertical cross section consisting of a stack of unit cells-is analogous to a measure in music. The regular pulse of a piece of music is given by the repetition of unit cells across the page. And the flow of a melodic line across measure boundaries is modeled by the flow of a visual line-such as the mountain-range lines-across many unit cells. Bach's music is always called up in discussions of the relation between mathematical patterns and music, and this occasion is no exception. I am reminded particularly of some of Bach's texturally more uniform pieces, such as certain preludes from "The Well-tempered Clavier," where in each measure there is a certain pattern executed once or twice and possibly more times. From measure to measure this pattern undergoes a slow metamorphosis, meandering in the course of many measures from one region of harmonic space to far-distant regions and then slowly returning by some circuitous route. For specific examples you might listen to (or look at the scores of) Book I, No. 1 and No. 2, and Book II, No. 3 and No. 15. Many of the other preludes have this feature in places, although not for their entirety. Bach seldom deliberately set out to play with the perceptual systems of his listeners. Artists of his century, although they occasionally played perceptual games, were considerably less sophisticated about, and less fascinated by, issues we now deem part of perceptual psychology. Such phenomena as regrouping would have intrigued Bach, and I sometimes wish he had known of certain effects and had been able to try them out, but then I remind myself that whatever time Bach might have spent playing with newfangled ideas would have had to be subtracted from his time for producing the masterpieces we know and love, and so why tamper with something that precious? On the other hand, I do not find this argument 100 percent compelling. Who says that if you are going to imagine playing with the past, you have to hold the lifetimes of famous people constant in length? If we can imagine telling Bach about perceptual psychology, why can't we also imagine adding a few extra years to his lifetime to let him explore it? After all, the only divinely imposed (that is, absolutely unslippable) constraint on Bach's years is that they and Mozart's years add up to 100, no? Hence if we give Bach five extra years, then we merely take five away from Mozart. It is painful, to be sure, but not all that bad. We could even let Bach live to 100! (Mozart would never have existed.) Although it is difficult to imagine and impossible to know what Bach's music would have been like if he had lived in the 20th century, it is certainly not impossible to know what Steve Reich's music would have been like if he had lived in this century. In fact, l am listening to a record of it right now. Now, Reich's music really is conscious of perceptual psychology. All the way through he plays with perceptual shifts and ambiguities, pivoting from one rhythm to another, from one harmonic origin to another, constantly keeping the listener on edge and tingling with nervous energy. Imagine a piece resembling Ravel's "Bolero," only with a much finer grain size, so that instead of its having roughly a one-minute unit cell it has a three-second unit cell. Its changes are so tiny that sometimes you can barely tell it is changing at all, whereas at other times the changes jump out at you. What Reich piece am I listening to? Well, it hardly matters, since most of his music satisfies this characterization, but for the sake of specificity you might try "Music for a Large Ensemble," "Octet" or "Violin Phase."

P. 18. Perhaps irrelevantly, but I suspect not, the names of many of these studies remind me of pieces by Zez Confrey, a composer best known in the 1920's for his novelty piano pieces such as "Dizzy Fingers" and "Kitten on the Keys" and - my favorite - "Flutter By, Butterfly." Confrey specialized in pushing rag music to its limits without losing musical charm, and some of the results seem to me to have a saucy, dazzling appeal not unlike the jazzy appearance of this parquet deformation.

P. 18. Incidentally, I know of no piece of visual art that better captures the feeling of beauty and intricacy in a Steve Reich piece, created by slow "adiabatic" changes floating on top of the chaos and dynamism of the lower-level frenzy. Looking back, I see I began by describing this parquet deformation as "calm." Well, what do you know? Perhaps I would be a good candidate for one of The New Yorker's occasional notes titled "Our Forgetful Authors." More seriously, there is a reason for this inconsistency. One's emotional response to a given work of art, whether the work is visual or musical, is not static and unchanging. There is no way of knowing how you will respond the next time you hear or see one of your favorite pieces. It may leave you unmoved or it may thrill you to the bone. It depends on your mood, on what has recently happened, on what happens to strike you and on many other subtle intangibles. One's reaction can even change in the course of a few minutes. And so I won't apologize for this seeming lapse.

P. 20. Comparing the creativity that goes into parquet deformations with the creativity of a great musician, Huff writes: "I don't know about the consistency of the genius of Bach, but I did work with the great American architect Louis Kahn (1901-1974) and suppose it must have been somewhat the same with Bach. That is, Kahn, out of moral, spiritual and philosophical considerations, formulated ways he would and ways he would not do a thing in architecture. Students came to know many of his ways, and some of the best could imitate him rather well (although not perfectly). But as Kahn himself developed he constantly brought in new principles that brought new transformations to his work, and he even occasionally discarded an old rule. Consequently he was always several steps ahead of his imitators who knew what was but couldn't imagine what will be. And so it is that computer-generated 'original' Bach is an interesting exercise. But it isn't Bach-that unwritten work that Bach never got to, the day after he died."

Writing lovely melodies is another one of those deceptive arts. To the mathematically inclined, notes seem like numbers and melodies like number patterns. Therefore all the beauty of a melody seems as if it ought to be describable in some simple mathematical way. So far, however, no formula has produced even a single good melody. Of course, you can look back at any melody and write a formula that will produce it and variations on it. But this is retrospective, not prospective. Lovely chess moves and lovely melodies (and lovely theorems in mathematics) have this in common: every one has idiosyncratic nuances that seem logical a posteriori but are not easy to anticipate. To the mathematical mind chess-playing skill and melody-writing skill and theorem-writing skill seem obviously formalizable, but the truth turns out to be more tantalizingly complex than that. Too many subtle balances are involved.

3. Anon. Science Digest, 1984, Vol. 98, Page 19, 25? Issues 7–9.

A full bibliographic reference is not available, all that is known is on Google Books, as above. The issue month is not stated.

Although music is not mentioned as such, this is indeed implied, with words such as ‘composer’ and ‘composition’.

How to read a fylfot flipflop

A parquet deformation is not a warped apartment floor; it's an ingenious problem in design. The basic elements are called tiles: squares, hexagons or other polygons that form a grid, like floor tiles laid congruently in a repeating pattern. But for the students in William Huff’s design course at the State University of New York, Buffalo, such a design is only the beginning.

Their task is to subtly deform the tiles, step by step, so that they change as the design is read from left to right. “I look at it somewhat the way a composer might look at his composition”, says Huff. “I tell students to let their eye tell them whether it's flowing or not, then we look at the design analytically. What are the events? How long does it take to get from one to another? What are the rhythms?”

An event is an eye-catching configuration… [Missing text]

...return of the square, but with the swastika reversed-the final event.

There are other interesting discoveries to be made about vertical and horizontal lines. After 20 years, says Huff, “I come to these new each time.”

[Caption] HOW TO READ THIS FYLFOT FLIPFLOP. TURN IT COUNTERCLOCKWISE. A fylfot is a swastika. In this design, called a parquet deformation, the fylfot reverses at the right.

4. William S. Huff, ‘Students' work from the Basic Design Studios of William S. Huff’. In Intersight One. State University of New York at Buffalo, 1990. 10, pp. 80–85.

Two mentions of music analogies.

P. 82. The whole composition of a parquet deformation is not intended to be viewed spatially, but temporally -- as a kind of visual music. The Oriental scroll paintings are one of the great few temporal, visual compositions. Viewing one, then, is akin to the manner in which film is seen, poetry read, and music heard.

The text here borrows heavily from the text of the earlier ‘The Parquet Deformation The Mirror-Rotation Symmetry’, 1979, of which for the sake of convenience I repeat below:

The total compositions are not intended to be viewed spatially, but temporally, as a sort of visual music. The Oriental scroll paintings are one of the great few temporal, visual compositions. Viewing them, then, is akin to the manner in which film is seen, poetry read, and music heard.

5. Charles Talley (Editor). Surface Design Journal - Volumes 16–17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.

NOT SEEN, GOOGLE BOOKS REFERENCE

Snippet view on Google Books:

P. 10. The incremental pace of change in a parquet deformation is rather like that of days moving one season to the next. Hofstadter notes its temporal character, equating a parquet deformation to visible music. The underlying principle seems to be …

One mention of musical analogies. Refers to Hofstadter's article. Essentially inconsequential.

6. William S. Huff. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag 1996, pp. 307–314.

As with Hofstadter's piece (q.v.), this is required reading.

P. 307. Though they occupy graphic formats, these designs are, by virtue of their

disproportionate horizontal dimensions, appreciated more as temporal than as spatial compositions

-manifesting a distinct affinity with the nonplastic arts of music, dance, poetry, and theater.

P. 307. This, I reflected, is contrary to classical Western dramatic structure, characteristic of theater, music, and dance.

P. 308. The temporal arts (music, dance, poetry, theater) occupy the dimensional space of the instantaneous present,...

P. 309. Music, linearly regulated in respect to time, does have spatial elements (notes and chords).

P. 310 (Quoting Nelson Hu) These components in their analyzed form, simple and pure, are universalities, behaving like musical tones, favoring no particular culture or tradition and belonging to all.

P. 312. In the case of our deformations, the contours are the object; they make the music. Fill between these contours with colors, textures, or figurative subjects-the music crashes.

7. William S. Huff. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010.

One mention to music analogies, referencing back to ‘The Landscape Handscroll...’.

The Experience of Timing

On previous occasions, I gave oral and written accounts of a type of design, regularly assigned in my basic design studio—the parquet deformation—which disposes time to participate as an integral third dimension, thus dynamizing the two-dimensional spatial content of the design. Commentary on the aesthetic potential of the parquet deformation was presented at the Katachi 2 conference (Huff 1994: 219-222), and commentary on its geometric requisites was presented at the SEMA 4 conference (Huff 2003: 9). I liken the parquet deformation to a remarkable art form, the Chinese handscroll, which, in its most exceptional, but younger genre, the landscape handscroll, goes back a thousand years. Time unfolds as the scroll is synchronously unrolled and rolled—pleasurable frame by pleasurable frame—not dissimilarly to how music flows. Time is engaged, however, in a different manner in respect to compositions whose three dimensions are all spatial.

8. Stavros Laparidis. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012, P. 22.

19 Example 5. Étude 9: Vertige, opening seemingly static but constantly changing type of music as “parquet deformation,” a very insightful term to describe this compositional design…

GOOGLE SCHOLAR REFERENCE, OSTENSIBLY ON PROQUEST. REQUESTED ON RESEARCHGATE

One mention of music analogies. Only a part-preview is available on ProQuest, of which just the first 13 pages are viewable. Although likely of a mention just in passing, of interest due to one of the few non-Huff/Hofstadter music discussions.

References

[*] Anon. Science Digest, 1984, Vol. 98 Page 19, 25?

[*] Hofstadter, Douglas R. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20.

[*] Huff, William S. The Parquet Deformation The Mirror-Rotation Symmetry, 1979.

[*] Huff, William S. ‘Students' work from the Basic Design Studios of William S. Huff’. In Intersight One. State University of New York at Buffalo, 1990. 10, pp. 80–85.

[*] Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’. In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag 1996, pp. 307–314.

[*] Huff, William S. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010, 128 pp.

[*] Laparidis, Stavros. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012, P. 22.

[*] Talley, Charles (Editor). Surface Design Journal - Volumes 16-17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.

2. Dance/Choreography (5 distinct authors, 14 references)

Douglas R. Hofstadter. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20.

P. 18. Let us now look at "Cucaracha," executed by Jorge Gutierrez at SUNY at Buffalo in 1977. It moves from the utmost geometricity-a lattice of perfect diamonds-through a sequence of gradually more arbitrary modifications until it reaches some kind of near freedom, a dance of strange, angular, quasi-organic forms.

The only (perhaps surprisingly) reference to dance (or any derivative) in the paper.

William S. Huff. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry, 1996, pp. 307–314.

P. 307. Though they occupy graphic formats, these designs are, by virtue of their disproportionate horizontal dimensions, appreciated more as temporal than as spatial compositions - manifesting a distinct affinity with the nonplastic arts of music, dance, poetry, and theater.

P. 307. This, I reflected, is contrary to classical Western dramatic structure, characteristic of theater, music, and dance.

P. 308. The spatial arts (painting, sculpture, architecture) occupy two-dimensional or three-dimensional real space. The temporal arts (music, dance, poetry, theater) occupy the dimensional space of the instantaneous present,...

Gabriele Brandstetter and Marta Ulvaeus. ‘Defigurative Choreography: From Marcel Duchamp to William Forsythe’. The Drama Review, Winter, 1998, Vol. 42, No. 4 (Winter, 1998), The MIT Press, pp. 37–55.

Inconsequential. Brief mention (not illustrated) of parquet deformations (in Hofstadter's Metamagical Themas) on pp. 48–49 in the context of dance.

Pp. 48–49. In terms of the relation of figure and space, the patterns of such choreography reveal a similarity with the designs that are known as "parquet deformations" (Hofstadter 1985:195-218): gradually developing transformations of divisions of the plane, or tessellations, which, through the lengthening or rotating of a line or through the introduction of a hinge, result in a complete distortion or regrouping-like a type of ornamental morphing.

Background of The Drama Review

TDR traces the broad spectrum of performances, studying performances in their aesthetic, social, economic, and political contexts. With an emphasis on experimental, avant-garde, intercultural, and interdisciplinary performance, TDR covers performance art, theatre, dance, music, visual art, popular entertainments, media, sports, rituals, and the performance in and of politics and everyday life.

Karl Schaffer. ‘Dancing Deformations’. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pp. 253–260

On the analogies of dance with parquet deformation. Not illustrated with Huff-type examples. Also see a like later paper of his, ‘Dichromatic Dances’, of 2017. Such comparisons are rare. Also, see Gabriele Brandstetter and Marta Ulvaeus on the same theme.

P. 253:

Abstract

The performing art of dance employs symmetry in a variety of ways. Often choreographers blur the lines between symmetries or seamlessly morph from one symmetry type to another. This may be seen to be similar to parquet deformations, visual images in which one tiling deforms seamlessly into another…

Parquet Deformations. The artist M.C. Escher created a number of works in which one tessellation morphs into another. Later in the 1960s the architect William Huff investigated these designs with his students, and received wider attention when explored and written about by Douglas Hoffstadter [4]. Recently Craig S. Kaplan has presented his investigations of them at Bridges [6]. These visual designs usually change seamlessly in a horizontal direction through several tiling patterns. Dance choreographers often utilize similar deformations, in both time and space.

P. 260:

[4] Douglas R. Hofstadter, “Parquet Deformations: Patterns of Tiles that Shift Gradually in One Dimension,” Scientific American, 1983.

[6] Craig S. Kaplan, “Curve Evolution Schemes for Parquet Deformations,” Bridges Proceedings, 2010, pp 95-102.

https://archive.bridgesmathart.org/2014/bridges2014-253.pdf

Karl Schaffer. ‘Dichromatic Dances’. Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, pp. 291–298

On the analogies of dance with parquet deformation. Not illustrated with Huff-type examples.

P. 291

Abstract

...This paper investigates danced two-colored or dichromatic symmetry patterns, and continues an earlier investigation on how such danced symmetry patterns may be seamlessly morphed from one symmetry type to another, in a manner similar to visual parquet deformations...

Introduction

....In this paper, I extend to two-colored or “dichromatic” patterns an exploration into danced parquet deformations [9], in which symmetric patterns of dancers morph from one pattern to another without breaking symmetry.

P. 292

… The earlier paper [9] examined how this may allow parquet like deformations from one symmetric dance formation to another.

P. 293

Figure 3 shows a “parquet deformation” sequence of positions for 4 dancers from a recent dance by the author titled “Blacks and Whites,” using possible two colorings of the one-color designs from Figure 2…

https://archive.bridgesmathart.org/2017/bridges2017-291.pdf

References

Brandstetter, Gabriele and Marta Ulvaeus. ‘Defigurative Choreography: From Marcel Duchamp to William Forsythe’. The Drama Review, Winter, 1998, Vol. 42, No. 4 (Winter, 1998), The MIT Press, pp. 37–55.

Hofstadter, Douglas R. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20.

Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry, 1996, pp. 307–314.

Schaffer, Karl. ‘Dancing Deformations’. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pp. 253–260.

Schaffer, Karl. ‘Dichromatic Dances’. Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, pp. 291–298.

3. Poetry (3 district authors, 4 references, plus 2 out of context)

William S. Huff, ‘Students' work from the Basic Design Studios of William S. Huff’. In Intersight One. State University of New York at Buffalo, 1990. 10, pp. 80–85.

Two mentions of poetry analogies.

The text here borrows heavily from the text of the earlier ‘The Parquet Deformation The Mirror-Rotation Symmetry’, 1979, of which for the sake of convenience I repeat below:

William S. Huff. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry, 1996, pp. 307–314.

P. 308. The temporal arts (music, dance, poetry, theater) occupy the dimensional space of the instantaneous present,...

Douglas R. Hofstadter. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20.

P. 17. "Dizzy Bee," executed by Richard Mesnik at Carnegie-Mellon in·1964 [page 15], involves perceptual tricks of another kind. The left side looks like a perfect honeycomb or, somewhat less poetically, a perfect bathroom floor.

‘Poetically’ is used figuratively here, and so is out of context re parquet deformation, but is included for the sake of having been ‘seen and noted’.

P. 18. The poetic term "flickering clusters" comes from a famous theory of how water molecules behave, in which the bonds are hydrogen bonds rather than mental ones.

Again, ‘Poetic’ is used out of context re parquet deformation, but is included for the sake of having been ‘seen and noted’.

References
Hofstadter, Douglas R. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20.

Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry, 1996, pp. 307–314.

4. Theatre (1 distinct author, 3 references)

William S. Huff. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry, 1996, pp. 307–314.

P. 307. This, I reflected, is contrary to classical Western dramatic structure, characteristic of theater, music, and dance.

P. 308. The temporal arts (music, dance, poetry, theater) occupy the dimensional space of the instantaneous present,...

N.B. Theatre/Theater is not mentioned in Hofstadter.

References
Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry, 1996, pp. 307–314.

Conclusion

By far of the performing arts, analogies are most frequently to be seen and discussed with music, almost to the near exclusion of the other performing arts. Both Huff and Hofstadter make insightful comments that add much to the interpretation. I'm not sure that I would have realised this if it wasn't pointed out, and likely others would be in the same position too. That said, this is perhaps largely for the connoisseur; it is possible to compose without this knowledge. However, a study of this perhaps ‘secondary’ aspect can only add to the understanding and interpretation of the parquet deformation, and as such is warmly welcomed.

Page History.

Page created 30 August 2021. Note that the text is largely built on an existing essay of 12 April 2021, solely on music, posted on a generic Essay page, as detailed above.

The working Google document is titled ‘Parquet Deformation and Performing Arts Analogies 30 August 2021’.

Comments