Fitting designs (continued)

Further to Fitting designs - which looked at the history of the classic puzzle of making an object that will fit three holes of different shapes: square, circular, and triangular - Emily from the largely mathematics/nature blog Ephemeral Curios commented:

These might also be the inspiration for Douglas Hofstadter's "trip-lets"-- the blocks on the cover of Godel, Escher, Bach that cast three different letter shadows.

Thanks! Yes, the GEB "trip-let" (left) is identical in concept to the object with three orthogonal letter shapes objects spelling "PSM" in Popular Science Monthly for July 1927 (see Arthur L Smith's A Square Peg in a Round Hole).

But I'm not clear if (as is quite possible) it was independently conceived; Hofstadter wrote in the intro to GEB:

The trip-let idea came to me in a flash one evening as I was trying to think how best to symbolize the unity of Gödel, Escher, and Bach by somehow fusing their names in a striking design. The two trip-lets shown on the cover were designed and made by me, using mainly a band saw, with an end mill for the holes; they are redwood, and are just under 4 inches on a side.

Does "idea came to me" mean the whole trip-let concept, or just the idea of using it for the cover?

There are plenty of interesting spin-offs. Googling found a nice page by Humberto José Bortolossi of the Mathematics Department, Universidade Federal Fluminense - Triplets - which has rotatable models, along with an intriguing reference to the generalisation of the idea. Objects can exist with an arbitrary number of specified shadows when illuminated from different directions. This is not merely theoretical, but has actually been applied to the creation of the "digital sundial" designed by Scharstein, Scharstein and Krotz-Vogel: see U.S. patent 5,590,093 and Digital Sundials International.

Another good page is The magic of trip-lets at mariano tomatis blog, which shows the design (not trivial to achieve) of an "EMC" triplet for the Eseential Magic Conference. It also raises the possibility of trip-let type objects in the past - that is, objects designed to look different from different directions - via the example of a 17th century carved crucifix by the Franciscan monk Fra Innocenzo da Petralia, deemed miraculous for its ability to show different expressions on the face of Christ (suffering, dying and dead) according to viewing angle. This looks to me an equivalent of the "Noh Mask Effect": the ability of masked actors to convey expression change in Noh drama by tilting the head to give different viewpoints of their rigid masks. See Michael J Lyons, Noh Masks & Facial Expression Perception, which has several research papers. The concept seems to be pretty widespread: see, for example, Perceiving faces of Buddha statues, Same miraculous statue; different expressions, and How Moving Light Changes Expression on Face of Small Statue.

- Ray

Of academic interest

Current reading: The Annotated Alice, Martin Gardner's classic concordance to Alice's Adventures in Wonderland and Through the Looking Glass: a compilation of both books, with Gardner's detailed annotations on Carroll's contemporary references to mathematical, poetic and scientific topics.
      The Annotated Alice is a fascinating insight into the books. This excerpt at Norton Books gives a taster of the annotations. The book is 47 years on from its first publication, and has seen continuing updates. A recent development has been the discovery of a lost chapter, The Wasp in the Wig that appears to have been deleted because Tenniel, the illustrator, wasn't keen on it. The Alice Project quotes this chapter along with theories about what Tenniel disliked. I especially like the explanations of the parodies. Carroll's nonsense verse in funny in itself, but more so when compared to the pious improving poetry that it quite viciously satirises (see The poems in Alice in Wonderland for comparisons such as How doth the little crocodile vs. How doth the little busy bee).
      The Annotated Alice isn't to everyone's taste: Will Self's New Statesman review of the new Definitive Edition, Dirty old man, takes a hostile view of its avoidance of the always fraught question of Carroll's sexual orientation. This is by no means a clear issue. For instance, nowadays we are highly cautious, paranoid even, about the motives for child photography and tend to view Carroll's interest in this as automatically suspect; but it was a highly mainstream genre in Victorian times. Furthermore, the predominant view that Carroll was some flavour of repressed paedophile was heavily shaken in 1999 by Karoline Leach's book In the Shadow of the Dreamchild, which argued that much of the accepted view of Carroll is a stereotypical myth created in the vacuum left by his family's destruction and suppression of biographical material. Recently published letters and his diary (see "Lewis Carroll": A Myth in the Making) present a picture of a man who was neither shy nor reclusive, and whose female friends were mainly adult, these relationships in some cases skating on the edge of scandal. It's hard to assess whether this view will prevail, but the evidence coming from the increasing flow of primary sources looks at least likely to modify the traditional assessment. More on this evidence at Looking for Lewis Carroll and Contrariwise.

Not terribly related, except as an academic pursuit: this morning a customer asked - perhaps having seen the recent Times article, Nocturnal missions - about a book we didn't have, The Night Climbers of Cambridge, by the pseudonymous 'Whipplesnaith'. It's an underground classic in Cambridge, a book written in the 1930s about the illicit ascent of colleges and other buildings. I admit it rather takes me back. Many Cambridge undergraduates need to do at least some climbing due to the older colleges' archaic practice of locking the gates at night, and I remember those terrifying revolving spikes that topped some walls.

Night Climbers is online at InsectNation: interesting reading, akin to the accounts of present-day urban explorers. Andy Buckley, the site creator, admits that the copyright is a bit 'grey', but risked it given that all persons and companies related to the book are defunct.

Addendum: The Night Climbers of Cambridge was reprinted in 2007 by Oleander Press, Cambridge, to mark the 70th anniversary of the original edition.

- Ray