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Pale Fire, repetition, IPH and PHI - posting number Two
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Extracts from an exchange at the D. Barton Johnson list, 27 September,2003 with "more Bernoulli links to Pale Fire" and recent postings:
Carolyn: First my apologies to Pynchoner David Morris who found the Bernoulli lemniscate before I did. Euclid discovered the number phi but Bernoulli discovered its relation first to the to the golden rectangle and then to the beautiful spiral that is formed by smaller and smaller golden rectangles built within each other -- the logarithmic spiral which he called miraculous.
Bernoulli ended his paper on this spiral with the words "eadem mutata resurgo semperdem [Though changed, I return over and over again the same]." These words (minus the un-Christian semperdem) are engraved on his tombstone in the cathedral in Berne.
If IPH = phi and Bernoulli discovered and named the lemniscate curve, then perhaps "eadem mutata resurgo" also has something to do with Pale Fire.
Jansy: Keithz has brought up Mircea Eliade and Carolyn Kunin has given special notice to patterns of repetition and to the idea of " though changed I return over and over again the same" in connection to Pale Fire. Mircea Eliade has written extensively on the Myth of Eternal Recurrence and about ancestral cyclical time versus historical time [ in particular, I remember the part he describes the curative effects of "ritually repeating an ancestral gesture" to "enter the time of the gods".]
JM : Content to have been informed "fractails" ( VN's Post-script in "Lolita") and "fractals" are not related, I also re-learned from the past that IPH and PHI were related to Bernouilli and to leminiscate curves.
Now these "golden rectangles built within each other" also brought to my un-mathematical mind images of "tesselation" and VN's idea about the spiral as a kind of glorified circle. Also Escher's engravings ( in particular the mixture bt. background and image in harlequin butterflies, puddles and self-referential or recurrent patterns...)
Kinbote used (as if inter-changeable) PH for HP in "Pale Fire" and in "LATH" we find the hero unable to deal with space and time, incapable to reverse his bodily position to view HP as PH...
Any help from experts to link IPH and Bernouilli, leminiscate and tesselated mosaics to the sensuous world of veiled mothers and kissing lips?
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Carolyn: First my apologies to Pynchoner David Morris who found the Bernoulli lemniscate before I did. Euclid discovered the number phi but Bernoulli discovered its relation first to the to the golden rectangle and then to the beautiful spiral that is formed by smaller and smaller golden rectangles built within each other -- the logarithmic spiral which he called miraculous.
Bernoulli ended his paper on this spiral with the words "eadem mutata resurgo semperdem [Though changed, I return over and over again the same]." These words (minus the un-Christian semperdem) are engraved on his tombstone in the cathedral in Berne.
If IPH = phi and Bernoulli discovered and named the lemniscate curve, then perhaps "eadem mutata resurgo" also has something to do with Pale Fire.
Jansy: Keithz has brought up Mircea Eliade and Carolyn Kunin has given special notice to patterns of repetition and to the idea of " though changed I return over and over again the same" in connection to Pale Fire. Mircea Eliade has written extensively on the Myth of Eternal Recurrence and about ancestral cyclical time versus historical time [ in particular, I remember the part he describes the curative effects of "ritually repeating an ancestral gesture" to "enter the time of the gods".]
JM : Content to have been informed "fractails" ( VN's Post-script in "Lolita") and "fractals" are not related, I also re-learned from the past that IPH and PHI were related to Bernouilli and to leminiscate curves.
Now these "golden rectangles built within each other" also brought to my un-mathematical mind images of "tesselation" and VN's idea about the spiral as a kind of glorified circle. Also Escher's engravings ( in particular the mixture bt. background and image in harlequin butterflies, puddles and self-referential or recurrent patterns...)
Kinbote used (as if inter-changeable) PH for HP in "Pale Fire" and in "LATH" we find the hero unable to deal with space and time, incapable to reverse his bodily position to view HP as PH...
Any help from experts to link IPH and Bernouilli, leminiscate and tesselated mosaics to the sensuous world of veiled mothers and kissing lips?
Search the archive: http://listserv.ucsb.edu/archives/nabokv-l.html
Contact the Editors: mailto:nabokv-l@utk.edu,nabokv-l@holycross.edu
Visit Zembla: http://www.libraries.psu.edu/nabokov/zembla.htm
View Nabokv-L policies: http://web.utk.edu/~sblackwe/EDNote.htm