On 17/12/2013 9:04 PM, Raul Miller wrote:
I think what you are talking about here is a concept of context:
We can think of 1j2 as a vector. We can also anchor that vector at the
origin and think of it as denoting a position. We can think of the
difference between two positions as a vector.
Absolutely true
Adding more dimensions means we cannot use a single complex value to
represent the vector, but more general concepts still hold.
Also true
Anyways, euclidean norm can find the length of two independent vectors
or, if we treat both as positions we can use euclidean norm on a
vector which is the difference of the other two, yes?
Yes
Euclidean norms apply to a given vector. If you have two vectors, then
you can find the norm of the each vector
or the norm of the distance between them which is the vector distance
between them. In fact you can find the norm of the sum ,product etc of
these two vectors because these are also 2D vectors.
What en does incorrectly in this case is essentially replacing two
vectors in a 2D space by a vector in a 4D space - as the old story when
Mr Wong looked at his wife and child "2 Wongs don't make a white".
'a b'=:1j2 4j10
a,b,b-a
1j2 4j10 3j8
|a,b,b-a
2.23607 10.7703 8.544
which is the length (norm) of each vector and of the difference as you
surmised correctly.
en a
2.23607
en b
10.7703
en b-a
8.544
en a,b
11 which, as far as I can see is meaningless.
Don
Or am I overlooking a key issue (again)? Thanks,
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