[PD] basic DSP stuff

Martin Peach martinrp at vax2.concordia.ca
Fri Nov 11 23:11:46 CET 2005

Chuckk Hubbard wrote:

> What I'm getting at is that expressing rotation as complex numbers is 
> no different than using cartesian coordinates.  Why, when you multiply 
> two points, would one of the multiples turn negative?
> I see no reason you couldn't say i = 1/0.  Then 4*0*i=4.  That makes 
> as much sense.

<OT lecture_and_rant>
Not really. Any number multiplied by zero becomes zero. You can't break 
the existing rules. There is a philosophical need for i because 
intuitively every number ought to have a square root, even negative 
numbers. The other philosophical need comes from the idea that the 
energy of an oscillator should be constant if the oscillator is at a 
constant amplitude and frequency, but the observable output of the 
oscillator passes through zero, which implies there is no energy there. 
Where is the energy? In an imaginary dimension...imaginary just means 
unobservable. This is basically how in quantum mechanics one decides 
what is actually observable versus just virtual, so there is some 
connection with reality here, but it's probably hard to grasp since 
humans have never used such concepts until about a hundred years ago 
simply because there was no practical use for them.
It also took a long time for people in Europe to accept the concept of 
zero after it had been invented in North Africa and Central America and 
elsewhere...in Roman numbers (I, II, III, IV...) there is no zero but in 
Arabic numbers (0,1,2,3,) there is. The Maya used a shell glyph for zero 
and dots and bars for the other numbers. I wouldn't get hung up on the 
use of i, it's like using an empty shell for zero, a kind of handle on a 
concept. Some people think that concepts cannot be expressed in a 
language that doesn't already have words for them, but they are wrong. 
The concepts are just expressed in a crooked, crooked way.
</OT lecture_and_rant>


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