[PD] basic DSP stuff
badmuthahubbard at gmail.com
Sat Nov 12 02:35:40 CET 2005
By the same token, any number times itself is non-negative. i breaks
existing rules too. (lol)
You know, I could just have said, oh, since you're multiplying i times i the
result is negative, by definition, and accepted that it works. I could just
be the kid who writes down what the teacher says and memorizes it for the
test, instead of asking questions. I suspect there is something else at work
for the result to be correct, because the only reason given for using i was
to represent the vertical axis. At no point was there actually a quantity of
-1, for which we found the root before multiplying by the second part of the
On 11/11/05, Martin Peach <martinrp at vax2.concordia.ca> wrote:
> 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>
"It is not when truth is dirty, but when it is shallow, that the lover of
knowledge is reluctant to step into its waters."
-Friedrich Nietzsche, "Thus Spoke Zarathustra"
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