Cognitive Bias and Claims of Quasiperiodicity in Traditional Islamic Patterns

Abstract

n this article I discuss whether traditional Islamic geometric patterns exhibit the distinguishing structural properties of quasicrystals. I present two case studies that examine candidate examples from the western and eastern schools of Islamic ornament. In both cases, researchers hypothesized that the Islamic patterns have quasiperiodic features, both found that their models did not match the data, yet both found reasons to discard the errors and to accept their model rather than to search for an alternative explanation. This has led to widespread confusion about the status of claims concerning quasiperiodic Islamic ornament, a situation that became clear to me during discussions at a conference, and that motivated me to write up these notes.In both case studies, the language and tools of crystallography are applied to analyse Islamic patterns. In each case I shall show that the conclusions are incorrect, and I shall also propose a different method of construction that agrees with the evidence and the wider context. The analysis of crystals is based on statistical properties of large samples, and real-world crystals display a range of defects when compared to our mathematically perfect models. I suggest that approaching the problem from a crystallographic perspective predisposes the mind to regard defects as anomalies rather than errors. This bias, together with flaws such as confirmation bias in the methodology, may explain how the researchers reached their conclusions. QuasiperiodicityA quasicrystal is a solid whose structure has long-range order that is not periodic, a property demonstrated by a diffraction pattern with sharp spots and symmetry that violates the crystallographic restriction. 1 Levine and Steinhardt [16] modelled quasicrystals as solids with three properties: long-range correlation in the orientation of atomic bonds, a mass density function that is quasiperiodic (a sum of periodic functions with incommensurate periods), and a local finiteness condition. On a global scale, such structures have no translational symmetry-each atom occupies a unique position different from any other. However, there is repetition of bounded neighbourhoods. We can find ''quasitranslations'' that almost overlay the structure onto itself; the proportion of mismatches can be made arbitrarily small by using longer translation vectors. In two dimensions the discrepancies can be made visible as Moiré patterns. There are also centres of ''quasirotational'' 1 Centres of rotational symmetry in periodic structures must be twofold, threefold, fourfold, or sixfold.

Darb-e Imam Tessellations: A Mistake of 250 Years

“…This 1453-dating of the Safavid tessellations has been persistent: see, e.g., Lu and Steinhardt (2007), Zheludev and Ozbay (2007), Saltzman (2008), Dewar (2009), Ferrero et al (2009), Juhel (2012), Todesco (2012), Al Ajlouni (2012Ajlouni ( , 2013, Au-Yang and Perk (2013), Tennant (2014), Topper (2014), Ebrahimi and Aliabadi (2015), Williams and Ostwald (2015), Aube (2016), Bier (2011Bier ( , 2012Bier ( , 2017, Cromwell (2015Cromwell ( , 2016, Caste ´ra (2016), Makovicky (2007Makovicky ( , 2016, Bonner (2017), Lissek et al (2017), Pautze (2017), Wichmann and Wade (2017). 9 In addition, it seems that Bonner's (2003) claim that four designs (his Figs.…”

Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

“…Nevertheless, imputing a nascent quasicrystal theory to medieval mathematicians simply cannot be justified based on historical records [61]. Other views support the presence of self-similar quality in some IGPs [62][63][64][65], making it somewhat similar to the structural signature of quasicrystals. Scholars like Cromwell [66] and Chorbachi [10] believe Islamic artists have had the tools to construct quasiperiodic designs without the theoretical framework to appreciate the possibility or significance of doing so.…”

Looking at Islamic Patterns II: Making Sense of Geometry

“…Although 'spot the flaw' experiments show that humans can identify a range of structural violations in rule-based patterns [118], we do not notice when Penrose tiles are assembled incorrectly. Trying to find evidence of quasiperiodicity in traditional Islamic patterns has been a cause of confusion and controversy [33]. The apparent complexity in Figure 15 is generated by six iterations of a small recursive PostScript program -very little information is required.…”