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Re: Query: interesting association
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On 19/12/06 16:35, "jansymello" <jansy@AETERN.US> quoted from VN¹s Bend
Sinister:
> The square root of I is I.
JM: another sweet tease to add to my growing folder ³VN and Mathematics.²
The lowercase I used in expressing the complex number (x + iy) represents
the square root of minus 1, to which the term imaginary¹ was misleadingly
applied to contrast them with real¹ numbers alas, these terms have
persisted, greatly confusing the general public. VN¹s little joke seems to
play on i-the-imaginary-number and I-the-possibly-unreal-EGO, as posited by
the Viennese Delegation!
The first thing that would attract a mathematician¹s attention is the
leading definite article THE, implying only ONE SQUARE ROOT for I. Taking a
square root normally gives TWO solutions. E.g., if I is indeed a square root
of I, so is I (minus I). I and I (minus I) are ONLY equal if I = 0 (zero).
So, if we take VN¹s ³THE square root of I is I² literally¹ (or rather,
mathematically!), it reduces to the POSSIBLY INTENDED proposition that ³I is
zero.² At least, it¹s a very arcane way of eliminating the authorial I.¹
Supposing VN meant ³A square root of I is I²: this allows the solution I = 1
(one) since 1-squared is certainly 1! This is also plausibly related to VN¹s
musings on undivided-monism, solipsism and ego (I) as NUMBAH ONE¹ (using
the college sports spelling.)
If VN had in mind i-the-imaginary-square-root-of-minus-one (it does occur in
general, non-technical writing, e.g., Einstein¹s own popular introductions
to Relativity), then the statement is false. Since i-squared is minus 1,
i¹s-square-roots cannot be +-or-minus-i. If I haven¹t lost you, getting the
FOUR square-roots-of-(i-the-square-root-of-minus-one) means solving the
quadratic equation x^4 + 1 = 0;
using EULER¹s MOST beautiful & mysterious formula e^(i*pi) = -1, we obtain
x = +/- 1/(2^(1/2)(cos pi/4 +/- i*sin pi/4).
Stan Kelly-Bootle
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Sinister:
> The square root of I is I.
JM: another sweet tease to add to my growing folder ³VN and Mathematics.²
The lowercase I used in expressing the complex number (x + iy) represents
the square root of minus 1, to which the term imaginary¹ was misleadingly
applied to contrast them with real¹ numbers alas, these terms have
persisted, greatly confusing the general public. VN¹s little joke seems to
play on i-the-imaginary-number and I-the-possibly-unreal-EGO, as posited by
the Viennese Delegation!
The first thing that would attract a mathematician¹s attention is the
leading definite article THE, implying only ONE SQUARE ROOT for I. Taking a
square root normally gives TWO solutions. E.g., if I is indeed a square root
of I, so is I (minus I). I and I (minus I) are ONLY equal if I = 0 (zero).
So, if we take VN¹s ³THE square root of I is I² literally¹ (or rather,
mathematically!), it reduces to the POSSIBLY INTENDED proposition that ³I is
zero.² At least, it¹s a very arcane way of eliminating the authorial I.¹
Supposing VN meant ³A square root of I is I²: this allows the solution I = 1
(one) since 1-squared is certainly 1! This is also plausibly related to VN¹s
musings on undivided-monism, solipsism and ego (I) as NUMBAH ONE¹ (using
the college sports spelling.)
If VN had in mind i-the-imaginary-square-root-of-minus-one (it does occur in
general, non-technical writing, e.g., Einstein¹s own popular introductions
to Relativity), then the statement is false. Since i-squared is minus 1,
i¹s-square-roots cannot be +-or-minus-i. If I haven¹t lost you, getting the
FOUR square-roots-of-(i-the-square-root-of-minus-one) means solving the
quadratic equation x^4 + 1 = 0;
using EULER¹s MOST beautiful & mysterious formula e^(i*pi) = -1, we obtain
x = +/- 1/(2^(1/2)(cos pi/4 +/- i*sin pi/4).
Stan Kelly-Bootle
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