AOG Gallery – It's this weekend !!!

A view from the art gallery balcony.

Scaled Labour

 The building of scale models is a enjoyable pastime. There is something pleasing about seeing big things in a tinier form. For one thing their overall shape can be better appreciated if we can see them from a kind of 'imaginary distance'. More and more, people are enjoying seeing drone footage for this same 'model-like' perspective. What is useful about models and miniatures however is that an understanding of the method of constructing, say of boats, planes, houses, or almost every sort of thing you can think of, can often better be achieved (and the full scale project be then tackled with more knowledge) if several scale models have been made before the real thing is realized to proper scale.

Dry stone bridges are no different. A lot can be learned about how to build them, and why and how an arch works, when you go about  constructing a model one first. If they are built outside in some natural setting, an imaginary scene can be created too where small crevices in rocks, or spaces between boulders, are made to appear like deep ravines or canyons. This is kind of a magical thing.

When I first saw the deep criss-crossing cracks in the surface of the limestone bedrock on Inisheer Island I felt like I was flying over it, looking down on a vast canyon/plateau landscape. The rugged contour of the Aran Islands has a fractal quality that enables one to imagine the geology on a smaller, or bigger, scale. 

I chose to build my tiny bridge over a 30 cm wide gap I found, which was a natural crack, about a metre deep, running through a slab of bedrock sloping down to the sea. I hoped the miniature would make the ‘gap' look like a life-size bridge spanning a huge chasm. 

I chose a spot far enough from the path that people would not be aware of it unless they were looking for it. Having the bridge too close to the path too would mean people would see it more from directly above, rather than looking across at the bridge, which is how we most often view them.

I used a plastic bucket, wedging rocks in the gap below it, to support it so that half the bucket appeared above the surface of the bedrock.

I had already collected suitable pebbles and all kinds of tiny flat stones, in that very same bucket, along the trail on my walk to the my tiny bridge site.

Both approaches to the bridge (the tails) were built up carefully with thin stones then I laid in a radiating pattern over the bucket form ‘ the centering’ with tiny v shaped stones, laid in proper voussoir pattern. The inside of the bridge vaulting was done just the same way I would do a full scale bridge, but on a tiny scale.

I paved the whole upper surface with one or two layers of thin flat stones. Most of the them could have made good skipping stones if I’d not been in a tiny bridge building frame of mind.

I came back later and landscaped with tiny plants and paved it again this time with gritty sand.

I had brought along my thumb sized, plastic Dr Who on the trip, and pulling him from my pocket, placed him standing by the bridge. It looked appropriately like he had been transported from some other dimension of space and time.

The mysterious miniature bridge was discovered by all kinds of people the weekend I was there on the island. Kids played with Dr Who, walking him up over the chasm and back. Observant curious tourists took plenty of photographs. 

That part of the path became a bit of a favourite stopping place for the horse drawn carts. Visitors aboard could ponder the tiny structure from their seats and perhaps merely wonder why someone would be so crazy to spend all that time making it. I guess it all has to do with scale and perspective. 

While I was making it, time stood still.  I became small enough to explore that small patch of  island bedrock as if I’d shrunk to an Inisheer fraction of my normal size

The Vandal Playground Area

I was called to come and repair a decorative dry stone bench we built a while back for a conservation area. It was built well enough and looked quite attractive. It was just that it looked a bit too attractive to vandals. Being in a remote area of a park where only a few people ever walk it was the perfect structure to try to demolish without getting caught doing it. 




It occurs to me that a special part of the park could be designed and built to be a 'Vandal Playground Area'. Dry laid walls and benches and cool features could be constructed within a well-defined concrete walled-in area. Those who felt the need to wreck things could come there at certain designated times and make havoc in a controlled environment where supervisors could watch and make sure no one got hurt.

After every 'session' (perhaps ever other day) those whole like to build things, or practice making attractive dry stone features, would be allowed to come and fix up the vandal playground area again. 

There would be a small fee for both groups being allowed to come there, either to build with the stones again, or wreck what was built.

Putting the pieces together

On a kind of whim one afternoon, while I was on Inisheer, I began looking for the other half of a stone I had found on the rocky shore, amidst all the other stones lying around. The odds of me finding it were very very slim, and yet amazingly after searching the area for about five minutes, I discovered its mate. The two pieces fit together so that barely any crack appeared.

And yet the reunited halves were not one stone again, they were two cracked stones. 

We can not put rocks and stones back together. We only break them or make them smaller with hammers. There is no way to make a stone bigger. We can't make them whole again either. We can't make them at all!

But we can make stone walls! We can cause the stones even the ones we've broken to be fitted to become a bigger whole – a beautiful whole.

And in this respect, making walls is very much like making bridges. It is positive inclusive thing. It's like making friends.  It's how healing happens too. Building walls is a way of making connections and seeing connections. In the end we discover a pleasing network of joints rather than just seeing cracks everywhere.

O the distance !

Life's like a road that you travel on
When there's one day here and the next day gone
Sometimes you bend, sometimes you stand
Sometimes you turn your back to the wind
There's a world outside every darkened door
Where blues won't haunt you anymore
Where the brave are free and lovers soar
Come ride with me to the distant shore
We won't hesitate, break down the garden gate
There's not much time left today

Life is a highway
I want to ride it all night long
If you're going my way
I want to drive it all night long

Shade

Yes, we can't work without light.

But we can't work without 'shade' either.

We can't actually see without shades of light. Without some sort of  shade from the hot glaring penetrating light, we'd be blinded and yes baked.

We really can't live without the benefit of 'blessed shade'. We'd all get burned up.

Certainly this hot blistering sun-brilliant weekend there would be not much stonework accomplished on the sun-baked walling workshop site if there wasn't some sort of shelter from the direct rays of the sun.

Even so our energy is sapped and many of us are dripping with sweat. 

But we press on, endeavouring to make something beautiful.

A place to rest. A bench to sit on and relax and enjoy the warmth of the sun perhaps, some day later in the fall, out of the shade, when its offer of relief will be shunned because it will feel too cold !  

Big and Small Walling

2017 Dry Stone Festival: St. Mark's, Barriefield/East Kingston Bring the family and watch a heritage restoration of a stone wall. Free dry stone workshops for kids. Tour Barriefield Village and St. Mark's, see the stone carving demos or drop in to the School Museum. There's lots to see and do.

There is also a two-day walling workshop for a hands-on learning experience! Cost for the workshop (including food, entertainment and optional lectures): $300. See Dry Stone Canada for details and to register.

As in other years, there will be a special children's walling activity again this year, both days of the 2017 dry stone wall festival, involving the creating of lots of miniature 'dry pebble' walls, huts, and bridges. Parents are invited to watch, but really, this is the 'Kids Only' part of the festival. Kids make sure your parents mark down the dates September 30th - October 1st on their calendar, and remember to bring you to our 'It's a small wall after all' event coming up NEXT weekend!

Sketches

Sketching the walls on the Aran Islands last weekend was an Inisheer joy, though I think drawing stones can sometimes seem harder than actually building with them. Our group comprised of Canadians Brits Austrians Americans and Irish enthusiasts (about ten people in all) tacked most of the lichen encrusted sites on the island including the 15 century tower house and an old sunken church. 

Much time each morning and afternoon was spent wrestling with line tone texture and perspective, (and all the other shades of artistic expression available to the imagination) intent on extracting the essence of this tiny island's timeless panorama of fantastical stonework, all majestically battered by harsh sun wind and sea. Eventually our attempts to get our individual 'islands' of watercolour paper to appear alive with a semblance of limestony likeness of the island paid off. 

Like doing stonework, time and persistence yielded some impressively expressive creations. 

We, the struggling artists didn't struggle too much in terms of food and snacks either. There were copious tea breaks in the shelter of the walls we were drawing, and biscuits eaten hastily nestled together out of the wind and rain, and yummy lunches of cheese and ham sandwiches to fortify the body and give everyone fresh resolve to get our heads around the walls, around the fields, and sea all the way around everything, we were trying to draw. 

Our competent volunteer sketch class 'leaders' were a talented couple from Dublin Jessica Peel-Yates and James Francis Moore (resident artists on the island this summer) who helped draw out our individual talents. As our three day drawing adventure drew to a close, we were all encouraged by the results, and resolved to definitely finish some of the rough sketches we had started on the island and maybe try to continue drawing and painting when we got home or perhaps even draw Inish'more' the next time we returned to the islands. 

Thanks again to Patrick McAfee for coming up with this not too sketchy of an idea and basically organizing this ruggedly creative adjunct to the festival of stone this year on Inisheer - Feile na gCloch 

Check out the blog that Jessica and James have at

https://inisheerzibaldone.wordpress.com/blog/

An Irish Instagram friend

Fergus Spackman, an excellent Irish mason and dry stone waller (and new Instagram friend) picked us up at the ferry from Inisheer yesterday and drove us around the hauntingly beautiful Irish countryside near Galway. We were shown some fine examples of walling including this arch that he built near Oughterard on Lough Corrib 

A string of rustic walls with seating areas and benches surrounding his client's rural property were accented with wonder plantings and fine woodwork including this unique gate. 

Fergus works alone and loves walling on this emerald island. 

His dog Bandit seems to enjoy the walling lifestyle too.

The walls and dry stone features Fergus builds have a funky character much like the structures I enjoy creating. In fact there were a lot of similarities in our work and our outlook on such walling subjects as breakfast breaks versus lunch breaks, shunning mortared veneer, Dr who, the importance of music, refraining from overshaping over engineering stones, enjoying Instagram connections, working hard and playing hard. 

Life on Aran Islands

What do wallers draw?

So the first day of the Irish walling workshop on Inisheer went well. The new wall will be completed by Sunday.

Some of the full time wallers visiting the island this year chose the option to go off sketching this weekend instead.

What do you suppose is the subject matter they choose to draw when they get a day off?  Perhaps, the many dry stone walls on the island, you say?

Wrong! It is Ship wrecks.

This is The Plassey which ran aground off the coast of Inisheer back in 1960

Hands

Dancing With Their Hands

A thirty finger piece of fantastic mirror-like choreography. They have a great routine going. And so much better than shaking fists or giving the finger. The mind can learn a lot from this.

Goodness.

Below is the full online article examining in some capacity how the attractiveness of various differing arrangement of rocks in a garden can be actually measured.  Goodness! Pretty heady stuff. 

http://onlinelibrary.wiley.com/doi/10.1111/j.1468-5884.2011.00496.x/full

Abstract

In this study, we examined pattern goodness in natural scenes using stone arrangements in a Japanese rock garden. The results showed that the stone arrangement simulating the rock garden at the Ryoan-ji Temple and arrangements with a single stone deleted from that simulation were evaluated highly. These arrangements had a self-similar spatial structure, namely, covert regularity, or had simple structures in medial axis transformation. These arrangements also produced impressions of greater width and depth than other arrangements. In contrast, sector arrangements, which gave the most regular impression, were evaluated the lowest for goodness. This suggests that the pattern goodness of natural scenes or the artistic evaluation does not always correspond to overt regularity, often considered to determine pattern goodness. The most important finding is that two types of sector arrangement and two types of random arrangement were classified in their respective groups by integrated multiple impressions, although they did not have similar perceptual appearances. An intuitive judgment based on integrated impressions may allow us to notice the hidden order in spatial structures and obtain substantial understanding of the structure.

In Gestalt theory, goodness is central to understanding the way in which the visual system organizes and stores percepts (Palmer, 1991). Summarizing Wertheimer's idea, Koffka (1935) said that psychological organization will always be as “good” as the prevailing conditions allow. In fact, we perceive a pattern or shape having perceptual goodness rather than understanding the structure or shape and afterward judging its goodness.

However, goodness is an idea that is not easily defined. Perceptual goodness is related to concepts such as simplicity, regularity, stability, order, harmony, and homogeneity (Kanizsa, 1979; Koffka, 1935; Palmer, 1991). Gestaltists have shown such relations by presenting visual examples, which are often more effective than explanations using words. However, if we define goodness in a scientific manner, we must redefine these related concepts.

After the Gestaltists, many have attempted to define goodness in operational terms or in quantitative ways, for example, using geometrical properties like the number of lines, the degrees of corners, and position (Hochberg & Brooks, 1960; Wilson & Chatterjee, 2005), the amount of information (Attneave & Arnoult, 1956), redundancy (Garner & Clement, 1963), the amount of structural information (Leeuwenberg, 1969) and transformation structure (Hamada & Ishihara, 1988; Imai, 1977; Imai, Ito, & Ito, 1976). The experimental data generally fit with these theories as long as limited stimuli are used, such as experimentally controlled, simple, and meaningless geometric shapes and patterns.

However, definitions of goodness based on such spatial properties of shapes or patterns cannot explain the different goodness among patterns with similar spatial structures or individual differences in the same patterns (Matsuda, 1978). In fact, pattern goodness changes just by rotation of a pattern (Mitsui, Shiina, & Odaka, 2008). Pattern goodness can be reversed also based on whether the whole pattern is shown or each part is shown successively (Kodama & Miura, 2009).

To overcome this problem, instead of definitions using stimulus properties, the perceptual or cognitive processes of observers have been discussed, for example, perceptual organization (Kodama & Miura, 2009, 2011), mental workload or attention (Klein, 1982; Miura, 2007; Miura & Kawabe, 2004; Pomerantz, 1991), length of verbalization (Glanzer & Clark, 1962), the association value (Garner, 1974), meaningfulness for observers (Markovic, 2002; Wada, Oyama, & Yamada, 2000), and personal traits (Chipman & Mendelson, 1979; Nakaya & Fujimoto, 1984; Yamashita & Furusawa, 1993).

However, these concepts are often not independent of the stimulus properties. Rather, they are an aspect of two sides of the definition because the patterns or objects that can be processed using minimum energy have mostly simple or regular configurations or shapes.

It is more fitting to think of the concept of goodness as consisting of multiple aspects. Gyoba, Seto, and Ichikawa (1985) pointed out that there are two kinds of goodness or two aspects of goodness judgment. One is goodness related to geometrical regularity that is basically determined by symmetry. The other is goodness as an integrated impression, shown by the evaluation factor, which is often extracted using factor analysis. The former corresponds to the perceptual attributes of stimuli, and the latter corresponds to the synthesized evaluations made by observers. Kanizsa (1979) said that “there can be several criteria for describing this property (=goodness) and the selection of one criterion instead of another may lead to different results.”

In addition, goodness is dependent on the context. Nakajima and Ichikawa (2008) showed that aesthetic impression, a kind of goodness, changed if they used dot stimuli that had concrete meaning (e.g. a button) and were placed on natural images (e.g. textiles). Inoue and Miura (2000) showed that a pattern evaluated highly was a little more irregular, such as when natural images of brick walls were compared to geometric black and white brick patterns. For natural scenes or objects, the standards of goodness seem to change compared to those for geometric patterns or shapes.

Breakthrough research on goodness in natural scenes or art works was conducted by Taylor, Micolich, and Jonas (2000) and van Tonder, Lyons, and Ejima (2002). Taylor et al. (2000) analyzed abstract paintings drawn by Jackson Pollock using fractal analysis and found that invisible fractal structure contributed to good impressions of the artistry. It is noteworthy that covert order was critical in the impressions of artworks. However, the study by van Tonder et al. (2002) gives more direct suggestions about pattern goodness in natural images.

van Tonder et al. (2002) and van Tonder and Lyons (2005) applied medial axis transformation to the stone arrangement of the famous Japanese rock garden at the Ryoan-ji Temple and uncovered a multiscale self-similar structure like a dichotomously branched tree, which can often be found in natural scenes. They also found that the trunk of the tree-like structure passed close to the main viewing area, reportedly the best place to appreciate the whole garden. They suggested that “the hidden order” (a term used by Japanese architect Yoshinobu Ashihara (1986) seems to give us impressions of calmness and sophistication when appreciating the dry garden, although we cannot see the self-correlation structure of the stone arrangement directly. With regard to observers' mental activity, this self-correlation structure seems to facilitate the perceptual organization of the spatial structure, reduce the mental workload involved in seeing it, and offer a relaxing and comfortable impression. That is, goodness can be defined again from both the spatial properties of a stimulus and observers' mental mechanisms.

The discussion by van Tonder et al. (2002) and van Tonder and Lyons (2005), however, was theoretically based on computational analysis showing the covert spatial structure of various stone arrangements. The observers' impressions were not directly examined. Moreover, according to their theory, based on medial axis transformation, the observers' evaluations are independent of their viewing point. However, in real scenes, the impression of a garden changes according to the viewing point.

In this study, we examined pattern goodness in natural scenes using the simulated stone arrangements of a Japanese rock garden that were used in the research of van Tonder et al. (2002) and van Tonder and Lyons (2005). We discuss the following points. First, do hidden spatial structures affect the evaluation of pattern goodness? Second, are arrangements that include hidden order, for example, a self-correlating spatial structure, evaluated highly? Third, do evaluations from the viewing point from which observers usually appreciate the garden support the theoretical analysis of van Tonder et al. (2002) and van Tonder and Lyons (2005)? Fourth, is the evaluation of pattern goodness related to the impression of depth (space extension in front and back) and width (space extension to the right and left) of the garden? Reportedly, there are several perspective devices in the stone arrangement of the rock garden of Ryoan-ji that cause the small garden to appear deeper. This extended spatial impression resulting from the devised stone arrangement may contribute to a good impression of the garden.

Experiment

Method

Stimuli.  Using the software, LightWave 3D, we rendered a 2-D computer graphic (30 cm × 150 cm), imitating the rock garden at Ryoan-ji. We created eight variations of the stone arrangement according to the research of van Tonder and Lyons (2005) and van Tonder et al. (2002): A, the original arrangement surveyed by Oyama (1970), the researcher of dry gardens; B and C, arrangements with a single stone deleted; D, an arrangement with a single stone added; E and F, arrangements with stones at random; and G and H, arrangements with stones in sectors. It is speculated that the stones of Ryoan-ji were arranged in sectors so that gazes to each stone gather from the best place to appreciate the garden. The stone arrangements in all stimuli were created according to those of van Tonder et al. (2002) so that the obtained results can be compared with the simulation of the arrangement. We also added another original arrangement measured by Nishizawa (2006), which was more recently surveyed and is said to be closer to the actual stone arrangement of Ryoan-ji. These two measurements, however, basically produce the same spatial structure using medial axis transformation, although the spatial impression, in particular, the impression of spatial extent, is different. Thus, we used a total of nine arrangements as stimuli.

All the arrangements were computer-generated images, assuming the observer was sitting on the veranda (Figure 1). The camera (at the eye-level of the observers) was set 1.8 m off the ground and turned to where a back wall touches the ground. The location of the camera (at the viewing point of the observers) was set where the main stem of the tree-like structure, based on medial axis transformation, passed. van Tonder and Lyons (2005) stated that this point is the location of maximal Shannon information. Thus, we set the camera at the ideal place to appreciate the garden. To see the whole stone arrangement of the garden, the camera was turned 10 deg toward the center (Figure 2). All of the medial-axis structures corresponding to each arrangement are shown in Figure 1.

Figure 1. 

• Open in figure viewer

The stimuli of stone arrangements (right) and their spatial structures obtained using medial axis transformation by van Tonder et al. (2002) (left).

Figure 2. 

• Open in figure viewer

Position and angle of a camera for drawing the garden stimuli. Left: The camera position shown in a white circle from an overhead view. Right top: The camera angle from an overhead view. Right bottom: The camera angle from a side view.

Each stimulus was projected on a 120 cm × 160 cm screen and was viewed from 300 cm. We used the large screen instead of a monitor-size display to facilitate an impression more similar to the real setting, although the retinal images in this viewing condition were not larger than when actually viewing the garden.

Procedure.  To reduce visual distractions, the experiment was conducted in a dark room. Using the semantic differential method, each participant reported their impressions of the gardens using 12 adjective pairs (see Table 1) on a 7-point scale, at their own pace. The order of the presentations of the stimuli and the adjective pairs was randomized among the observers. Before the experiment, the observers viewed all stimuli, presented for 3 s each.

Table 1.  Results of the factor analysis: the factors related to appreciating gardens 

Adjective scale	Evaluation	Quiet	Regularity	Communality
Note. The numbers in bold indicate the adjectives pairs with the highest factor loadings.
Liked – disliked	.895	−.043	.106	.815
Good – bad	.890	−.024	.148	.813
Beautiful – unbeautiful	.838	−.101	.182	.746
Interesting – uninteresting	.674	.265	−.095	.534
Wide – narrow	.446	−.413	−.205	.699
Deep – shallow	.274	−.036	−.164	.280
Desolate – bustling	.007	.836	−.004	.613
Modest – brave	.216	.752	−.028	.411
Quiet – noisy	−.207	.487	−.018	.103
Regular – irregular	.081	−.040	.799	.465
Organized – disorganized	.025	.052	.600	.647
Simple – complex	−.064	−.466	.494	.363
Eigenvalue	3.46	2.48	1.80
Variance explained (%)	26.04	16.47	11.56
Accumulated variance explained (%)		42.52	54.08

Observers.  Thirty Japanese students (21 female and 9 male, mean age = 23.3 years) without special knowledge about Japanese rock gardens participated in this experiment.

Results

Stone arrangements with similar impressions.  Based on the data, we conducted cluster analysis using Ward's method to determine the arrangements producing similar impressions. The results, shown in Figure 3, indicated that there were three types of arrangements that resulted in similar impressions, namely, original and deletion arrangements (A, A′, B, C), sector arrangements (G, H), and random and addition arrangements (D, E, F).

Figure 3. 

• Open in figure viewer

The results of cluster analysis: the stone arrangements with a similar impression.

Factors related to evaluating stone arrangements.  We conducted factor analysis using unweighted least squares with Varimax rotation to determine the factors related to appreciating rock gardens. We extracted three factors based on both screen plot and Eigenvalues greater than 1. The results are shown in Table 1. The first factor comprised “liked,”“good,”“beautiful,” and “interesting.” Thus, we considered it the evaluation factor. The second factor comprised “desolate,”“modest,” and “quiet,” termed the quiet factor. The third factor comprised “regular,”“organized,” and “simple.” We considered it to be the regularity factor.

Relation between stone arrangements and impressions.  Based on the results of cluster analysis and factor analysis, we conducted a one-way analysis of variance (ANOVA) for the three groups of arrangements. Significant mean effects were found in all factor conditions: Evaluation: F(2, 358) = 33.637, p < .001; Quiet: F(2, 178) = 65.983, p < .001, and Regularity: F(2, 178) = 83.976, p < .001. Post hoc multiple comparisons using Ryan's method showed significant differences between every pair of groups for all factors (p < .05), as shown in Figure 4.

Figure 4. 

• Open in figure viewer

The results of the analysis of variance: the relation between the stone arrangements and the factors.

In the original and deletion arrangements, the averaged rating scores of the evaluation (goodness) and quiet factors were the highest. In the random and addition arrangements, the averaged rating scores of the quiet and regularity factors were the lowest. In the sector arrangements, the averaged rating score of the evaluation factor was the lowest, and that of the regularity factor was the highest.

Relation between goodness and impression of spatial extent.  Based on the rating scores for the adjective pair wide-narrow, we conducted a one-way ANOVA for the nine arrangements. A significant difference in means was found in impressions of width, F(8, 232) = 11.672, p < .001. Post hoc multiple comparisons using Ryan's method showed significant differences (p < .001) between A′-D, A′-E, A′-F, A′-G, A′-H, A–E, A-G, B-D, B-E, B-G, C-D, C-E, C-G, C-H, F-G; significant differences (p < .005) between B-H, G-H; and a significant tendency (p < .01) between B-F. Regarding the impressions of depth shown from the deep-shallow judgment, a significant tendency in the mean effects was found, F(8, 232) = 2.764, p < .01. Post hoc multiple comparisons using Ryan's method showed significant differences between A-G (p < .001).

The correlations of the mean evaluation value between goodness and width impression, and goodness and depth impression were 0.673 and 0.787, respectively, although these correlation coefficients were not significant.

All arrangements obtaining higher scores on the wide-narrow scale belonged to the original and deletion groups, as shown in Figure 5a. The highest score was obtained for the original arrangement using the measurement of Nishizawa (2006), and the lowest score was obtained for one of the sector arrangements. Regarding depth impression, the highest score on the deep-shallow scale was obtained for the original arrangement using the measurement of Oyama (1970), and the lowest score was again obtained for one of the sector arrangements (Figure 5b).

Figure 5. 

• Open in figure viewer

Scatter plot of the mean rating scores (a) between the goodness and the width impressions, and (b) between the goodness and the depth impressions. Circles: Original and deletion arrangements. Squares: Random and addition arrangements. Triangles: Sector arrangements.

Discussion

In this study, we examined pattern goodness using rock garden stimuli that were more realistic than the dot patterns typically used in studies of pattern goodness. The results show that a hidden spatial structure affected the evaluation of pattern goodness. The arrangement including a self-similar spatial structure (the original arrangement) was evaluated highly. Thus, the hypothesis by van Tonder et al. (2002) and van Tonder and Lyons (2005), based on medial axis transformation, was supported. Moreover, the goodness of the spatial arrangement was related to the impression of the spatial extent. The highly evaluated arrangements tended to be judged as wider and deeper.

The most noteworthy result in this study was that the spatial structures of stone arrangements could be correctly distinguished by intuitive and comprehensive impressions (Figure 3), although they could not be distinguished by perceptual appearance. That is, although the observers may not have noticed that the stones in G and H were arranged in sectors, they classified them in the same group. The two random arrangements were also distinguished from other arrangements. Intuitive judgment or insight seems to allow us to grasp spatial structures without awareness. Ashihara (1986) showed that certain covert proportions in depth and height (e.g. the depth of a street or the height of a building) give us particular spatial impressions. Similarly, certain covert spatial structures of the stone arrangements give us particular impressions, and these impressions are useful in distinguishing arrangements. We always pay attention not to spatial structure, but to the objects in it. However, not the objects in space (the figure), but the spatial structure itself (the ground) seems to be important for spatial impressions. Intuitive impressions can judge the covert spatial structure, without the distraction of attentive objects.

Arnhaim (1969) suggested that a judgment is already implicit in the seeing. In this experiment, it might be appropriate to say that a more accurate judgment is not in the seeing but in the feeling. However, as mentioned by Kanizsa (1979), expecting too much of unconscious judgment may be risky because it can cause us to make certain types of mistakes, for example, as shown by Shimojyo and Ichikawa (1989).

The second noteworthy result is that goodness does not always correspond to an impression of regularity, the total impression evaluated by the adjectives “regular,”“organized,” and “simple” in this experiment. In the case of the sector arrangements (Figure 4), the evaluation factor was the highest, although these arrangements were the lowest in pattern goodness. Goodness is often said to relate to geometrical regularities such as repetition and symmetry, or geometrical regularities are causes of goodness. Moreover, goodness is considered to relate to regularity not only in geometrical regularity but also in the comprehensive regularity shown in impressions. The rating score for the evaluation factor often corresponds to that of the regularity factor (Imai et al. 1976; Matsuda, 1978; Miura, 2007; Miura & Inoue, 2000; Oyama, Yamada, & Iwasawa, 1998), although each factor obtained using factor analysis is theoretically independent of the others. However, Nakajima and Ichikawa (2008) and Inoue and Miura (2000), both using natural images, showed that the peak of the evaluation scores deviated from the peak of the regularity scores. In addition, artistry judgment can be independent of regularity. Goodness judgment in this experiment might be related to the artistry aspect of the rock garden. Whether the results in this experiment were dependent on the stimuli of natural images or artistry judgment remains a question.

However, the original and deletion arrangements were evaluated highly, while the arrangements including complex structures using medial axis transformation were not preferred (Figures 1,4). That is, the self-correlative spatial structures or simpler and well-organized structures were highly evaluated in the goodness judgment. The hidden order or implicit regularity of spatial structures is considered to relate to the goodness judgment. Van Tonder and Lyons (2005) pointed out that natural patterns are often self-similar, but the shapes themselves are irregular and asymmetrical. An asymmetrical configuration, including hidden order, appears to be required for goodness of rock gardens. Too much regularity or vague symmetry seems not to be preferable.

Regarding the impression of spatial extent, the scores on the wide-narrow and deep-shallow scales suggest that gardens evaluated highly are rated high on both dimensions. It is reported that various means were used in designing the rock garden at Ryoan-ji that contribute to the narrow garden appearing wider. The height of the stones, the walls, and the trees gradually becomes lower from the front to the back (Miyamoto, 1998), while the height of the ground becomes higher from the front to the back. Such linear perspectives contribute to the impressions of depth in this garden. Biederman, Hilton, and Hummel (1991) pointed out that “goodness may be epiphenomenal, reflecting the operation of perceptual mechanisms designed to infer a three-dimensional world from parts segmented from a two-dimensional image and to provide descriptions of objects that can be recognized from a novel viewpoint or that are partially occluded.” The sector arrangement of G, evaluated the lowest, had a flat configuration in 3-D space, and all stones were visible. Subjective involvement in perception brings about positive impressions (Miura, 2007).

As for the impression of wideness, empty space (“Yohaku”) is considered to be a critical factor. However, the results of this experiment did not clearly show this. More controlled experiments should be conducted. Onaka and Matsuda (2006) pointed out that the panoramic impression and the perceived lateral distances differ in their qualities. We also posit that the extension of space in an impression is different from a perceptual extension such as the filled/unfilled illusion.

Last, we refer to the next step of this experiment. In this experiment, we showed all stones of a garden in one computer-generated picture. However, actually, we cannot see all the stones in the rock garden of Ryoan-ji at a glance while sitting on the veranda. We must turn our heads or walk through the veranda if we want to see all the stones in the garden. We use not only vision but also somatic sensation to appreciate this garden. Therefore, time, memory, and somatic sensation should be considered in goodness judgments of garden stimuli. Regarding the rock garden of Ryoan-ji, Nakaji (1999), a Japanese philosopher, said that “moving the viewing position just by several millimeters will give you other rich and beautiful spectacles that you didn't see before. At that time, you will understand that you will be surrounded and filled by unlimited spectacles in a natural scene. At the same time, you will also find that you can take in only one viewing point and one spectacle at a time.” The influence of motor sensation and time course on pattern goodness as well as goodness judgment from various viewing points is our next research problem.

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