Complexity in Chess Does Not Enhance Aesthetics

Complexity in Chess Does Not Enhance Aesthetics

Presented by Azlan Iqbal, Ph.D. Universiti Tenaga Nasional, Selangor, Malaysia.

Introduction & Review 

In 1977, a psychologist published a paper looking at the ‘principles of beauty’ using the game of chess as a domain of investigation.

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He consulted with expert players and used 23 pairs of chess positions.

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Among his many findings was that, “neither strangeness nor difficulty produces beauty” or basically, complexity does not enhance aesthetics.

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This challenged the idea most people – and certainly chess problem composers – had about ‘difficulty’ being a key ingredient in objects that were appreciated for their beauty.

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In chess, for example, if the solution is simple it is typically not considered by composers to be beautiful.

Introduction & Review 

Yet, the science on this issue suggested otherwise. Here are the some of the positions used in the 1977 research. Experts claimed they are of comparably beauty

Introduction & Review

Experts largely agreed 2(a) was the most beautiful despite requiring the least amount of calculation (i.e. difficulty) compared to (b) and (c) which they said required more calculation.

Aim 

So in our research, we wanted to verify if complexity, as a general principle of beauty, did not indeed enhance aesthetics.

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Now, 40 years later, the technology exists to measure this computationally using an experimentally-validated computational chess aesthetics model and automatic chess problem composer.

Chesthetica

Experimental Setup 

The method we employed was to test the compositions generated autonomously by Chesthetica in terms of how long a chess engine took to find the solution.

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The longer the engine took, the more complex the problem was assumed to be.

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The solving engine used was “Chest” v3.19 because it is a relatively small and particularly fast mate solver.

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We used two standard personal computers for all tests, i.e. a desktop running Windows 7 and a ‘notebook’ running Windows 10.

Experiment 1 

We tested two sets of compositions, i.e. mate-in-3 and longer mates which consisted of mate-in-4 and mate-in-5 problems.

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The hypothesis here was that longer mates inherently tended to be more complex and would therefore require a longer time for the engine to solve.

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After testing 52 generated compositions from each set on our desktop computer, we found there was indeed a statistically significant difference in terms of the engine solving time; twotailed Mann-Whitney U-Test, z = -2.6162, p = 0.0088.

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The three-movers took 0.2964 seconds, on average, for the engine to solve whereas the longer mates took 0.3169 seconds, on average.

Experiment 1 

This meant that we could not reject the hypothesis that longer mates do indeed, on average, require a longer engine solving time and that the engine could indeed be used as a measure of the complexity of a chess problem.

Experiment 2 

The second experiment, which ran on our notebook computer, therefore applied this knowledge (i.e. complex problems required longer solving time) in testing whether three-move problems that simply took longer to solve were more beautiful or aesthetic than three-move problems which could be solved more quickly by the same engine.

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The same idea should therefore be extensible to longer mates that took longer to solve compared to longer mates that were quicker to solve. We also tested these.

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The aesthetic scores were calculated by Chesthetica. These scores have been previously shown to correlate positively and well with domain-competent human assessment.

Experiment 2 

An optional feature was therefore included into Chesthetica which allowed it to generate more complex compositions by simply rejecting all the ones that had a shorter composing time than the average composing time so far.

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The first three compositions were used to get the baseline average and subsequent compositions were rejected if their composing time was not greater than that average.

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These were compared with compositions generated using the standard approach that did not favour complexity.

Results 

The details are shown in Table 1, with the number of generated compositions for each set provided in brackets.

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The results showed that in both cases (i.e. for threemovers and longer mates), the mean aesthetic scores were not different to a statistically significant degree regardless if complexity was favoured.

Conclusions 

Using modern experimental and AI techniques, we confirmed that complexity does not enhance or improve aesthetics (using chess as a domain of investigation).

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The confirmation of this finding is important because chess problem composers tend to assume that a more difficult problem (i.e. one with a more difficult solution) is more desirable aesthetically than an easier one.

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It therefore appears that this belief is not necessarily true, if true at all. So composers should focus specifically on other aspects or principles of beauty in the game if they wish to enhance the aesthetics of their compositions.

Conclusions 

The idea that difficulty may not or does not contribute to beauty may also extend to other domains of artistic endeavor.

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For instance, artwork that is difficult to interpret or appears confusing may be appealing to some experts but rarely to the larger population of people who appreciate beautiful art.

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It is quite likely that there are other simpler or more straightforward characteristics of beautiful art that can be capitalized on by artists in order to enhance aesthetics in their domain of creative endeavour.

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Future work may include experimental validation of such characteristics as being helpful aesthetically in contrast to complexity or difficulty in those specific domains.

Q&A

Thank you