Escher and the Droste effect

 

Samuel Verbiese2003-01-11 03:01:30
Here what I try to send to all conributors with valid e-mail addresses... I hope the project team will give their comments too !. Dear Escher admirers, Recently I discovered the most inspiring http://escherdroste.math.leidenuniv.nl site and the very interesting discussion going on in its guestbook, with more than eight hundred entries now, so I made sort of a summary with some new thoughts of mine they induced. You might be interested to have a look and further elaborate perhaps? If I unduly forgot or missed an interesting point you raised, please tell it right in the guestbook to relaunch the discussion. Please don't blame me to use English : Dutch is not the primary language of most Escher admirers in the world. I know I may say so, because a majority of Dutch people do have an excellent command of English ! Wasn't it abroad, by the way, that Escher got the first wide recognition for his work ? Mag ook toch gezegd worden : niemand was ooit profeet in eigen land... Now, in addition to what you will read in the guestbook, there were three other ideas coming to my mind, as I keep thinking about it all: 1. on Escher's print, there are exactly four sides on the frame of the exhibited print the young man is looking at, as it should be, the right one bursting open under the pressure of the gallery from the other side of the river that blows up towards us in coincidence with the one the young man is standing in. This looks yet another thought that makes me confortable with the original, and makes me believing as many of you do, folks, that the breathtaking work of this team does not "complete" the work of Escher, but gives it another direction... 2. ...THAT MOREOVER IS ITSELF "UNCOMPLETE" IN ESCHER'S OWN WORDS (see "The World of Escher" I cited in my last note in the guetbook and which I read so many years ago...). This new construction, as nice as it can be, indeed features only one infinite point, the very frame itself limiting arbitrarily the infinity behind us and on the sides, something that bothered Escher much in the years after he produced this print, and for which he only found a satisfactory solution in his print "Circle Limit III". Indeed, "Smaller and smaller I" that he made in 1956 a little after this famous "Print Gallery" features such a kind of one-sided infinity that left him unhappy... 3. ...despite the fact that he proved there that he was perfectly able to pursue convincingly to a very high depth the quality of this vanishing point. Three other reasons that seem to confirm that the blurred spot wasn't a shortcoming, but a deliberate choice, because the quest to infinity was probably not the purpose of this print. I thank sincerely all of you who had similar thoughts which brought me on "the good track" as I'm near to believe now. This doesn't diminish in any way the work done by this group, that not only is amazing in itself, but that helps us understand and admire even more how a genious Escher was without computers and advanced math education, thus constituting a real tribute to him ! Kind regards, Sam.