[PD] basic DSP stuff
cyborgk at nocturnalnoize.com
cyborgk at nocturnalnoize.com
Fri Nov 11 19:38:43 CET 2005
You could indeed say that "entity of your choice = 1/0". But you need a
compelling reason why such a quantity is useful, and various proofs on how
it is derived and used. All math depends on certain assumptions and those
assumptions are different in different circumstances - aka Euclidian
geometry and topology.
Actually, you can say 1+2 = 12 ... and if you are putting together a
string in a programming language, that makes sense and is useful, it is a
valid operation. Many object oriented programming languages let you
redefine basic symbols such as "+ - * /". But string addition wouldn't be
very helpful for doing audio math calculations.
So if you want to define your own i, go ahead, but don't you think your
calculations are going to turn out better if you follow the normal math
definitions?
~David
> 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.
>
> On 11/10/05, Mathieu Bouchard <matju at artengine.ca> wrote:
>>
>> On Mon, 7 Nov 2005, Chuckk Hubbard wrote:
>>
>> > Not that I don't appreciate the snide commentary, but this is why I'm
>> > asking. You can't forget the sin*sin part. i stands for "imaginary".
>> > (slowly: i is "imaginary"). Turning the product of sines into the
>> > negative product of sines is imaginary. There is no number that,
>> > squared, equals -1. There is no number that, squared, equals -1. It's
>> > not really there.
>>
>> depends on how people define "number". In math, it's usual to use an
>> extended definition which isn't so limited as to forbid sqrt(-1) from
>> existing.
>>
>> also, to understand the word "imaginary" in math, you have to first
>> understand that its meaning is completely distinct from any meaning of
>> "imaginary" outside of math.
>>
>> likewise for Real... "Real" is just a name. Small integers have a
>> relatively high tangible quality to them, but it gets mostly downhill
>> from
>> there. "Real" numbers are arguably much less tangible than integer
>> numbers, rational numbers, algebraic numbers, and then some. The numbers
>> PI and E are a lot more tangible than almost all (100%) of the Real
>> numbers.
>>
>> ____________________________________________________________________
>> Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
>> Freelance Digital Arts Engineer, Montréal QC Canada
>>
>
>
>
> --
> "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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