IMPLEXI MUNDI: International Arts and Sciences Complexity Worlds

Judgments of Time, Aesthetics, and Complexity as a Function of The
By: frederick david abraham on: Tue 01 of Jan, 2008 [20:52 UTC] (2426 reads)

In this experiment, we obtained judgments of the duration of presentation of 3D images of chaotic attractors, and judgments of their aesthetic value and complexity as a function of their fractal dimension (D2). We used four levels of fractal dimension (four stimuli at each level, mean D2s = .59, 1.07, 1.54, 2.27), with small samples of six students from each of three populations (elementary school students, graduate students, and special education students from ethnic minority groups in residence on our campus). In addition to replicating earlier studies of aesthetic judgments, we additionally asked for judgments of complexity to see if they were also a nonlinear function of the fractal dimensionality of stimuli (they were, increasing to a maximum at D2 = 1.54, and falling off at D2 = 2.27), suggesting the possibility that aesthetics and complexity judgments were at least in part mediated by perceived complexity. Perhaps this non-monotonic result was due to a loss of contrast and detail within the attractors at the highest dimensional complexity. Judgments of duration did not yield a significant F-ratio between groups, but t-tests showed the lowest dimensionality yielded shorter time estimates than those for the higher dimensionalities. If complexity is a determinant of subjective duration of these stimuli, it is saturated at fairly low levels of the fractal dimensionality of the stimuli. Three-way ANOVAs within participants, showed only the fractal dimension as a significant source of variation in aesthetic and complexity judgments. Academic level, gender, or cultural differences were not significant sources of variation in judgments, although there were some interesting individual and cultural findings.

http://www.blueberry-brain.org/silliman/JEM%20ms4.htm external link

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1. Introduction

1.1 Narrative Background

It was originally my intent to study the perception of time as a function of the fractal nature of stimuli, using auditory or musical stimuli, when Elliot Middleton informed me of a program by Julien Clinton Sprott that generated visual strange attractors, which I immediately downloaded from Sprott’s website, and was immersed in a world of beautiful images. We realized that by switching to these visual stimuli we could have a set of images whose fractal dimension was already computed by his program. I had been using his earlier book (Sprott, 1993) with the newly established Chaos Society of Silliman University, and so was familiar with his approach to dynamics, and with his research on aesthetics as a function of fractal dimension (Aks & Sprott, 1996). I later visited him while he adapted his programs to more general psychophysical explorations. While mainly interested in time perception, I had decided to use aesthetic judgments as well, mainly to attenuate the importance on time for my participants. Then I had the idea to add complexity judgments, thinking at the time that there were no precedents for that, which was true for such images, but in fact, I learned later, has a large history in psychophysical research. At any rate, he adapted his programs for me to be flexible to meet the changing needs of future experimental designs. When some undergraduate students at Silliman asked me for an idea for a research project using chaos for an experimental psychology course they were taking, the opportunity for them to do this exploratory study presented itself. About the same time, while giving lectures at a conference in Moscow in 2000 (Sulis & Tromifova, 2001), I shared Sprott’s computer program with Olga Mitina who subsequently did a nice study with it adding the investigation of personality factors (Mitina & Abraham, 2003). Thus began our collaboration.

1.2 Research Background

Nonlinear dynamical systems have recently been explored in cognitive and perceptual systems by the foundational programs of Freeman, (2006; Skarda & Freeman, 1987), Gregson (1996, 2006), Heath, (2000), Kelso and Engstrøm (2006), Turvey (2005), and Ward (2001), among many others. For a brief earlier history, see Abraham (1997a).

Perceptual/neural organizational features of attending complex stimuli may affect both the estimation of complexity and aesthetics, but also, there is the possibility that they could also affect the perception of time. There is likely a nonlinear interaction between the complexity of stimuli and experiencing time and aesthetics. Studies of both the perception of time and of aesthetics have centered on cognitive and biological factors (Anderson & Mandell, 1996; Eisler, A., 2003; Eisler, H.; Eisler, Eisler, & Montgomery, 1996). Many factors of stimuli, cognition, and biology have been investigated. One of the features of stimuli which make both biological and cognitive demands for time estimation is the amount of perceptual/cognitive effort involved, such as can vary with complexity of stimuli (Cupchik & Gebotys, 1988; Stoyanova & Yakimoff et al., 1987). The same could likely be said for aesthetic judgments (Aks & Sprott, 1996, 2003; Mureika, Cupchik, & Dyer, 2004; Sprott, 1993, 2003; Taylor, Spehar, Wise, et al., 2005).

To investigate the possibility of a relationship between complexity and judgments of time and aesthetics it was decided to use abstract stimuli. Chaotic attractors were used for this purpose as they are easy to generate along with objective measurements of their complexity (Aks & Sprott, 1996; Sprott, 1993a,b, 2003). Also, they are relatively free of prior associations. Chaotic attractors as stimuli can be created by integration of three coupled differential equations that produce abstract computer images in two spatial dimensions with the third dimension being represented by color coding, which adds to their aesthetic potential. To check on the assumption that mathematical complexity has a relationship to perceived complexity, it was decided to add an estimate of complexity to the ratings obtained from the participants.

While complexity of stimuli was the principal independent variable, demographic factors as well, namely age and culture (Eisler, Eisler, & Montgomery, 1994; H. Eisler, 1996) were also varied. Therefore, both children and adults, and both urbanized students of Silliman University and rural cultural minority visitors (Ati and Sulod) to a specialized education program to our campus served as participants.

And to enrich the dependent variable side of the experiment, in addition to scales of aesthetics and complexity, and estimates of stimulus duration, some narrative explorations of the features upon which the participants might have been basing their judgments were also attempted.

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davidgibson

On the judgment of time

on: Wed 30 of Jan, 2008 [14:56 UTC]

score: 4.75

"Perhaps this non-monotonic result was due to a loss of contrast and detail within the attractors at the highest dimensional complexity."

In the traditional CHC theory of intelligence, there are three kinds of "processing speed" measured: (Gs) The speed of executing automatized elementary cognitive processes; (Gt) reaction time for making decisions and (Gps) psychomotor speed (controlling movement independent of cognitive control as a piano player might move fingers).

I wonder if the complexity dimension interacts with one or more of these speeds on the way to the judgment of time?

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fredabraham

Re: On the judgment of time

on: Sat 02 of Feb, 2008 [01:09 UTC]

score: 0.00

> "Perhaps this non-monotonic result was due to a loss of contrast and detail within the attractors at the highest dimensional complexity."
>
> In the traditional CHC theory of intelligence, there are three kinds of "processing speed" measured: (Gs) The speed of executing automatized elementary cognitive processes; (Gt) reaction time for making decisions and (Gps) psychomotor speed (controlling movement independent of cognitive control as a piano player might move fingers).
>
> I wonder if the complexity dimension interacts with one or more of these speeds on the way to the judgment of time?

Fred's reply: Thanks for this useful insight. I had not tried to break down aspects of what would make for the cognitive appraisal other than point to obvious features of the stimuli. I think the first two would both be important. There have been studies of eye movements in aesthetic studies, including those with complex abstract stimuli and dynamics visual stimuli such as ours. You can bae sure I will include your suggestion in my discussion section. Thanks, David.

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fredabraham

electric sheep

on: Sat 19 of Jan, 2008 [01:34 UTC]

score: 0.00

Gus said: "Oh, and one reference I left off my comment on fractals and time: http://electricsheep.org/external external link

link for a very interesting evolutionary fractal pattern produced by multiple machines around the world."

We have a paper coming out on this:
Scott Draves, Ralph Abraham, Pablo Viotti, Frederick David Abraham, Julian Clinton Sprott. (2008 April).
The Aesthetics and Fractal Dimension of Electric Sheep
International Journal of Bifurcation and Chaos, 8(4).

I oversaw the data analysis and got Sprott involved initially for the dimensional analysis of the images, which were animated from iterated function systems. Ralph knew of Scott's work, and saw the relevance to the work that Clint and I did being reported here at our conference. I also had a lot of history and literature which got jettisoned from early drafts whichI wrote, but Scott got in a hurry for a fast publication, and the article is much abbreviated and in the letters section of the journal. The most exciting aspect of Scott's work is the evolution of aesthetic evolution over a changing large population of users in a distributed environment, and a changing population of images (the electric sheep). Among the many analyses, I was most interested in following these changes over time in the differenct groupoings of images, but these were not used in the publication. Too bad, this is the most interesting aspect. This was Scott's main interest, as you probably saw from his essays at his web site. Very sophisticated stuff.

When I first learned of his work, and went to his site, I had just finished reading Dick's Do Andorids Dream of Electric Sheep (dicussed in my Cybersexuality article, so what an amazing convergence that is.) These two articles here of mine converging to a single attractor, or maybe androids bifucating to two attractors, the social philosophic and the aesthetic evolutionary.

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GusKoehler

Re: electric sheep

on: Sat 19 of Jan, 2008 [19:04 UTC]

score: 0.00

Wow, Fred. Talk about coincidence. Could you e-mail me the article and your analysis of the evolution of the patterns?

> Gus said: "Oh, and one reference I left off my comment on fractals and time: http://electricsheep.org/external external link

link for a very interesting evolutionary fractal pattern produced by multiple machines around the world."
>
> We have a paper coming out on this:
> Scott Draves, Ralph Abraham, Pablo Viotti, Frederick David Abraham, Julian Clinton Sprott. (2008 April).
> The Aesthetics and Fractal Dimension of Electric Sheep
> International Journal of Bifurcation and Chaos, 8(4).
>
> I oversaw the data analysis and got Sprott involved initially for the dimensional analysis of the images, which were animated from iterated function systems. Ralph knew of Scott's work, and saw the relevance to the work that Clint and I did being reported here at our conference. I also had a lot of history and literature which got jettisoned from early drafts whichI wrote, but Scott got in a hurry for a fast publication, and the article is much abbreviated and in the letters section of the journal. The most exciting aspect of Scott's work is the evolution of aesthetic evolution over a changing large population of users in a distributed environment, and a changing population of images (the electric sheep). Among the many analyses, I was most interested in following these changes over time in the differenct groupoings of images, but these were not used in the publication. Too bad, this is the most interesting aspect. This was Scott's main interest, as you probably saw from his essays at his web site. Very sophisticated stuff.
>
> When I first learned of his work, and went to his site, I had just finished reading Dick's Do Andorids Dream of Electric Sheep (dicussed in my Cybersexuality article, so what an amazing convergence that is.) These two articles here of mine converging to a single attractor, or maybe androids bifucating to two attractors, the social philosophic and the aesthetic evolutionary.
>
>

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fredabraham

Gus on complexity, culture

on: Sat 19 of Jan, 2008 [00:38 UTC]

score: 5.00

Gus

Thanks for your interest in this unfinished article. You are right on the long germination. Very frustrating to blow out all else to concentrate on the literature search it demands. The time spent on these conferences doesn't help either, but the propect of seeing Anna and Hannes should push me some.

Complexity was an after thought to the experiment, added at the last minute. but is has turned up two very interesting finds. One is the experimental result. The other, is when I added it, I presumed that no one had asked the obvious: how would judgments of complexity relate to objective measures of complexity (D2).

The answer to the first relates to the ubiquitous finding of inverted U-shaped functions in psychology, drive levels, etc. This result has turned up in a lot of the recent studeis of aesthetics as a function of D. But our finding that complexity judgments have a similar inverted-U function suggests that aesthetics is a linear function of the perceived complexity. If you look at the figures we used (the one shown with the abstract above, you see a lot of internal boundaries and featuers that increase with D, the figure is the next highest we used, D=1.54. When you get to the highest, D=2.24, the space of each attractor is more filled (as dictated by the higher D), but there is less detail, more homogeneity, so it is judged less complex.

Next, as to my expectation of being first to measure complexity, it is true as far as I know from the recent dynamics studies, but it was well studied back in the 60s, by Berlyne among others. That research is mixed on finding the inverted-U, a passion of Berlyne. There is no relation to the grouping. There may be age and background effects yet to be found, but the conditions of the experiment were not conducive to finding them. There will be differences. Looking at individual results suggest that one could group results in a qualitative way. For example one of the graduate students is a faculty in art, and said he preferes open space, and his scores confirmed this. Similary one might expect those who like Chineese art that has much empty space, to yield similar results. Also, personal experience tells you that complexity alone is not going to be a sole factor in aesthetics.

On the study of time, Anna Eisler has included cultural issues as you know, and I hope she discusses these at the conference. And while our own result on time is non-significant, a dissappointment since that was the principal motivation for this study, and the princial reason for your interest in the study. But I was heartened that the odd curve was found by another study of time perception (I forget the authors at the moment, and that part of the paper is yet to get its full literature review).

Very perceptive questions and suggestions, and when we get together, we probalbly could develop some interesting time-perceptual experiments.

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GusKoehler

Judgements of Time

on: Mon 14 of Jan, 2008 [00:03 UTC]

score: 4.50

This paper has been a long time in germination. It is very satisfying to see how well Fred has connected the literature to his experiments. I don't quite understand the adding of estimate of complexity to the rating obtained from participants. How is this tied to the stimulus and its quantiative characterization and grouping? The cultural issue is very interesting, particularly in that different cultures perceive time very differently. Religion may also play a role here too (Christian vs. non-christian in the sense of not tracing itself to Judiac roots).

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