Re: Relativity and delusion

on Wed, 23 Jul 2008 17:06:41 -0400
<fd2dncxb0pr3ABrVnZ2dnUVZ_srin...@xxxxxxxxxxx>:
Dirk Van de moortel wrote:
No, I don't think so either - there will always be a steady fresh
supply of retiring engineers and highshool dropouts who learned
to handle a square root.
The high school dropout won't have learned about the complex
plane. The operations of multiplication for negative and imaginary
numbers have a perfectly reasonable picture, involving the rotation of
complex vectors.

Dirk,
What is the square root of -1?
How about -4?
Negative numbers can't have square roots huh?

I understand the definition of imaginary.
1) Most words have more than one definition. The use of the word is
determined by the context as interpreted by the people in the
discussion. When scientists are discussing an "imaginary number," they
are not using the definition of imaginary as something that doesn't
correspond to anything the physiccal world. They are using a a series
of definitions and operators defined. Go to any high school math book
for a definition of imaginary numbers.
2) Imaginary numbers are well defined on the complex plane, which
is quite larger than a number line. The complex plane is every bit as
"real" as a number line. Multiplication in the complex plane includes
rotation. A physical picture of the multiplication operation, as
defined on the complex plane, is available which may satisfy even you.
Multiplying two complex numbers includes rotation by the sum of their
phase angles.
3) The complex plane includes the entire number line, including the
negative numbers. On the complex plane, the product of two negative
numbers is a positive number. Multiplying two negative numbers
corresponds to adding their phase numbers, each 180 degrees. 180
degrees plus 180 degrees = 360 degrees, which on the complex plane
corresponds to the direction of the positive number line.
4) The next thing you will tell me is that matrix multiplication
doesn't exist. Hah!
.

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