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Re: children's rhymes
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On 23/06/2008 19:07, "jansymello" <jansy@AETERN.US> wrote:
> ... VN considered Gogol's prose as "four-dimensional, at least. He may be
> compared to his contemporary, the mathematician Lobachevsky ..." ( a
> biography of Nikolai Gogol by Vladimir Nabokov, New Directions Paperbook,l961
> (page 145).
> --------
>
> Jansy: an intriguing and understandable reference! But slightly misleading!
> Lobachevsky and Bolyai certainly "[co-]invented" Non-Euclidean Geometry
> independently**, but not in the 4-dimensional sense apparently implied by VN.
> Initially, Bolyai-Lobachevski Geometry simply described TWO-dimensional spaces
> that follow all of Euclid's axioms & postulates EXCEPT ONE (namely the Fifth
> postulate concerning the existence of parallel lines in 2-dimensions). By
> modifying this postulate, you can arrive at flat (Euclidean) or curved
> (elliptic or hyperbolic, Non-Euclidean) spaces. B-L geometries can be extended
> to higher dimensions, BUT SO CAN EUCLIDEAN GEOMETRIES! One must avoid
> confusing the concepts of dimension and euclideanism!! VN had in mind, I
> suppose, the emerging Theory of General Relativity with its 4-dimensional
> locally-flat but globally-curved space-time, since this was, in fact, the
> first practical and stunning application of B-L geometries to the real world,
> but unknown to Bolyai or Lobachevsky at the time. The impact of B-L on the
> history of science has been compared to that of Darwin! It is said that Gauss
> pre-empted B-L but hid his work -- he could not face the drastic
> theological/epistemological impact of denying the apodeictic "certainties" of
> Euclidean geometry!
>
> Sorry to make a meal of this, but my ongoing preoccupation is delving into
> VN's knowledge and mastery of mathematical ideas as opposed to his firm grip
> on matters biological/taxonomic.
>
> ** Rumours of L plagiarizing B and vice-versa are now generally discounted.
> YET, many listers will know mathematician Tom Lehrer's parody:
>
> "Who deserves the credit, who deserves the fame
> Nikolai Ivanovich Lobachevsky is his name ..." [Hoy!]
>
> "Plagiarize! Let no one else's work evade your eyes!
> Remember why the Good Lord made your eyes,
> Don't shade your eyes, but plagiarize! Plagiarize! Plagiarize!
> [spoken] Only be sure always to call it, please, 'research'!"
>
> skb
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> ... VN considered Gogol's prose as "four-dimensional, at least. He may be
> compared to his contemporary, the mathematician Lobachevsky ..." ( a
> biography of Nikolai Gogol by Vladimir Nabokov, New Directions Paperbook,l961
> (page 145).
> --------
>
> Jansy: an intriguing and understandable reference! But slightly misleading!
> Lobachevsky and Bolyai certainly "[co-]invented" Non-Euclidean Geometry
> independently**, but not in the 4-dimensional sense apparently implied by VN.
> Initially, Bolyai-Lobachevski Geometry simply described TWO-dimensional spaces
> that follow all of Euclid's axioms & postulates EXCEPT ONE (namely the Fifth
> postulate concerning the existence of parallel lines in 2-dimensions). By
> modifying this postulate, you can arrive at flat (Euclidean) or curved
> (elliptic or hyperbolic, Non-Euclidean) spaces. B-L geometries can be extended
> to higher dimensions, BUT SO CAN EUCLIDEAN GEOMETRIES! One must avoid
> confusing the concepts of dimension and euclideanism!! VN had in mind, I
> suppose, the emerging Theory of General Relativity with its 4-dimensional
> locally-flat but globally-curved space-time, since this was, in fact, the
> first practical and stunning application of B-L geometries to the real world,
> but unknown to Bolyai or Lobachevsky at the time. The impact of B-L on the
> history of science has been compared to that of Darwin! It is said that Gauss
> pre-empted B-L but hid his work -- he could not face the drastic
> theological/epistemological impact of denying the apodeictic "certainties" of
> Euclidean geometry!
>
> Sorry to make a meal of this, but my ongoing preoccupation is delving into
> VN's knowledge and mastery of mathematical ideas as opposed to his firm grip
> on matters biological/taxonomic.
>
> ** Rumours of L plagiarizing B and vice-versa are now generally discounted.
> YET, many listers will know mathematician Tom Lehrer's parody:
>
> "Who deserves the credit, who deserves the fame
> Nikolai Ivanovich Lobachevsky is his name ..." [Hoy!]
>
> "Plagiarize! Let no one else's work evade your eyes!
> Remember why the Good Lord made your eyes,
> Don't shade your eyes, but plagiarize! Plagiarize! Plagiarize!
> [spoken] Only be sure always to call it, please, 'research'!"
>
> skb
Search archive with Google:
http://www.google.com/advanced_search?q=site:listserv.ucsb.edu&HL=en
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
Visit "Nabokov Online Journal:" http://www.nabokovonline.com
Manage subscription options: http://listserv.ucsb.edu/