Möbius Strip II

This is of the 'basic model', of a half twist, albeit of a condition, with the edges touching at right angles to give a symmetrical 'figure of 8' composition. It will be seen that the print is intended (by Escher) to be presented in a portrait orientation, rather than landscape.

As sure as anything can be certain of the series, this, unlike the others, is indeed unequivocally a Möbius strip! Nonetheless, I examine the discussions.

Contributions are by Maurits Escher (2), Doris Schattschneider, Joseph Myers, Marjorie Senechal, and Jeffrey Price (2).

An endless ring-shaped band usually has two distinct surfaces, one inside and one outside. Yet on this strip nine red ants crawl after each other and travel the front side as well as the reverse side. Therefore the strip has only one surface.
Maurits C. Escher, Graphic Work, p. 12, within the category of 'Spatial Rings and Spirals'.

A straightforward, bare-bones description of the print, in line with other entries in the book.

Let us change the subject once more and see some prints with ribbons…To conclude this ribbon series [which also included Spirals, Sphere Spirals, Rind, Bond of Union], I show you two Möbius strips [Möbius Strip I and Möbius Strip II]. …The right slide shows a ribbon that is twisted only once. Nine red ants are walking in a continuous file, one after another, at both sides of the ribbon.
M. C. Escher, Escher on Escher, pp. 62, 64.

Escher also commented on the print (in tandem with Möbius Strip I), within the context of ribbons in text taken from his (abandoned) US lecture tour notes, 1964. I omit the distinct discussion on Möbius Strip I so as to not distract from Möbius Strip II. This is perhaps less than exact. 'twisted only once' is open to interpretation. A half twist or full twist? Also, Escher calls it (loosely?) a ribbon. No matter, he is clearly intending a Möbius premise.
Again, another bare-boned description, that is even more sparse than the Graphic Work entry. Although I would want more, the text has to be put into context overall. In both, this is not intended as an all-encompassing discussion of the various nuances but rather serves as an 'introduction'.

Certainly, there is no new insight from the above.

Möbius Strip II harbors a procession of ants crawling in an endless cycle. With a finite number of figures, Escher depicts infinity through the continuous traversal of an endless loop. The ants demonstrate as well that this unusual loop (originally printed vertically) has only one side.
Doris Schattschneider. 'Escher's Metaphors'. Scientific American, November 1994, pp. 66–71
A brief description without delving too deeply into the intricacies.

Möbius Strip II, 1963
Whilst this behaviour is most popularly exhibited by processionary caterpillars, ants also follow each other to a certain extent. In this woodcut, Escher populates the surface of a Möbius strip with a set of ants. Since the Möbius strip is non-orientable, the ants can see other ants walking on the underside of the surface. With an odd number (in this case, nine) of ants, the ants are directly between their subterranean counterparts; with an even number, equidistant ants form pairs with each ant immediately below its partner. Compare this with star polygons, which are connected if and only if the parameters are coprime.
Whilst reclining on the forbidden grass of our rivals, St. John's College, a dialogue developed about the one-sided nature of the Möbius strip. Specifically, I was looking through these Escher postcards and explained how to construct a Möbius strip by introducing a half-twist into a strip of paper before connecting the ends. The person to whom I was talking astutely remarked that the surface of an ordinary sheet of paper is also technically one-sided [since it is a topological sphere].
Joseph Myers, website

This is interesting in that Myers posits a reason for nine ants, an odd number, as opposed to showing an even number. He also gives a plausible reason for the choice of ants. Not only that, but peripherally, why a sheet of paper is, or can be, considered one-sided.

His famous woodcut "Swans" (which he adapted to the school pillar) is sometimes said to be a Möbius band but in fact it is a cylinder, and the ribbon-like "Horseman" is a figure eight. But "Ants" really is a Möbius band; the ants are crawling along a single surface.
Marjorie Senechal. Quoted in 'Escher Designs on Surfaces'. In M.C. Escher: Art and Science, pp. 103–105.

Upon assessing which of Escher's prints are or are not a Möbius strip, Senechal categorically asserts that Ants is.

Conclusion

All this clearly shows a Möbius strip is intended, without any quibbles or conditions.  Möbius Strip II does not have a single naysayer.

Created 17 May 2024. Last Updated 17 May 2024