Unanswered Escher Questions

Below I pose a series of questions that I have about various aspects of M. C. Escher and his works, the answers of which I have been unable to ascertain. Can anybody throw any light on these?

Q. 1
Why are Escher’s preparatory drawings/sketches that underlie the genesis of the periodic drawings rarely, if at all, shown? In just about all publications on Escher, these are notably conspicuous by their absence. Indeed, most books completely disregard them. As such, the only source for such material that I am aware of is Visions of Symmetry by Doris Schattschneider, who at least does show a few examples, pages 106-108 and 111, albeit even so, only page 111, showing the Horseman drawing, directly relates to the genesis of that particular periodic drawing. During the course of designing the periodic drawings, Escher must have composed many hundreds, perhaps even thousands of such sketches. Therefore, what has become of this material? Did Escher mostly dispose of such studies upon having completed the definitive periodic drawing? This seems highly unlikely given his general approach, with thoroughness in attention to detail and record keeping. Oddly, in contrast to the paucity of the above material, other preparatory drawings for Escher's non-tessellating ‘spatial structures’ (such as Depth and Spirals) are shown in various books in abundance - why such a discrepancy?

Q. 2
Escher frequently derided his mathematical ability, but beyond vague statements as to his lack of ability, his qualifications are not categorically stated. Is it possible to equate his school-day qualification to a present UK or USA standard?

Q. 3
What books on mathematics did Escher read/own? As such, I am unaware of any specific book. Although a list of the crystallographic journals he read is indeed given in Visions of Symmetry, page 337, there is no equivalent book list, either there, or to the best of my knowledge elsewhere. Was an inventory (personal or otherwise) made of his books?

Q. 4
Occasionally (specifically of drawings 18, 20-22, 25, 56, 59, 63, 66-67, 71-72, 80, 91 and 96), Escher lightly pencilled an ‘X’ next to the periodic drawing number (on the left hand side). As such, the denoted drawings, as regards their symmetry arrangements and/or motifs do not appear to be connected in any way as may be supposed by such denotation – therefore, what is its significance? 
Possibly related to this is that a similar ‘X’ (albeit circled) appears on two of the drawings (shown in Visions of Symmetry, page 17) he made upon his second visit to the Alhambra in 1936. Presumably, this was added retrospectively, as he would have had no need to mark the drawings in this way (as regards apparent cataloguing purposes) for such ‘early’ work when he was merely copying the tiles. If the 'Alhambra' and subsequent periodic drawings are indeed thus related to each other in this matter, then the relationship is not obvious.

Created: 29 March 2010

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