Escher's Themed Prints
Or
An Examination of Escher's Four Möbius Strip Themed Prints (or are sometimes said to be)
Introduction
The study began as an initial, focused study occasioned by an email of 27 December 2023 from the Escher authority Jeffrey Price, knowing my interest in Escher-like tessellations, querying if Escher's Horseman print was, indeed, a Möbius strip, with him having looked at the matter in some depth, and going to the trouble of a paper model recreation, and having doubts as to the premise (Fig. 1).
Perhaps you can help me understand Escher's Horsemen [print]. I wanted to get a better grasp on the structure of "Horsemen" so I made a band and taped it together. see photo. No twists were involved. I don't recall this being discussed in this way. DeRijk writes in Magic Mirror "In Horsemen, a three-colored woodcut made in 1946, we see a Moebius strip with two half-turns. If you make one for yourself you will find that it automatically forms itself into a figure-eight."I'm missing something. I trust DeRijk but I don't see a double-half-twist Moebius strip! What do you think? Is it a Moebius or a Nobius?
It is fair to say, by most, that Horseman is taken at face value as a Möbius strip. To this end, I thus took a look at the matter. At face value, it doesn't appear to be a particularly onerous study, of which it would appear that it can soon (a matter of an hour or so?) be swiftly resolved. However, this ideal proved to be highly wishful thinking! A few hours turned into a day, and then a day to days, and then a week to weeks, and a month to months (admittedly not studied exclusively and consecutively, with the study put aside for others). Nonetheless, much more time was spent on this than originally anticipated. And then the original remit, of my own volition, expanded into all four prints and expanded again with matters of the Möbius strip in the round, as shown on the site.
Although I was indeed familiar with Horseman and the other three prints, I had not previously made a special study of them of my own volition (I had commented on Horseman and Swans, in line with other tessellation-themed prints in my Escher essay series (in 2005), but this was not a 'special study' as such. Möbius Strip I and Möbius Strip II were not commented on at the time, being non-tessellations. Therefore, as is my custom in such circumstances, I surveyed and gathered the discussions for an overview. The research is largely confined to the major Escher books and authors, such as Ernst, Schattschneider, etc. Although (largely from the Internet Archive and JSTOR) there are other references, these seemingly are nothing more than a name check in passing, or if discussed in the proper sense of the meaning, are of a decidedly lower standard than 'the names'. Although not to be entirely dismissed, the law of diminishing returns would surely apply here; I simply do not have the time to check 'all'. If the answer is not contained in the major books and articles, it is unlikely to be found elsewhere. However, that said, on what was envisaged as the last day of the study (26 January) I found what I believe is the best (and most easily understood) description of all, including the mainstream publications, on a website! In normal circumstances, such references, usually from hobbyists, are treated with caution; however, the owner, Robert Ferréol, is not merely a (well-informed) 'hobbyist' (as in most cases), but is a more than respected mathematician (a professor), and so this gives gravity to his point of view. And then to better understand the Möbius strip I continued with an ever-widening remit, purely out of interest. This began an intense phase, of reading, practical works, new findings, rereading, in a loop. No matter what, I do not unduly begrudge the time spent on it. It has led to new insight into the intricacies here, as well as a general expansion of a generic Möbius strip regarding the Escher-like aspect.
Created 13 May 2024. Last Updated 13 May 2024