Ah, that brings back memories. Looked at some posts by Erik Naggum and they certainly didn't disappoint. What I miss about Usenet is that there was no limitation to the length of posts and you could choose whatever client you wanted (of course being open to ridicule and hostility if you chose wrongly).
semitone
@semit0ne
- 52 Followers
- 66 Following
- 317 Posts
Jack of many trades, master of no one. You can create art and beauty on a computer.
@simon_brooke I don't see the connection. My (admittedly limited) understanding ist that in an intuitionistic setting you don't define the natural numbers differently but you use intuitionistic logic to prove propositions in arithmetic.
Let's pretend we had the natural numbers augmented with the symbol infinity. What is the element of this set that when added to "infinity" gives 0, i.e. the additive inverse of "infinity"?
@simon_brooke You can do anything you feel like, but beware that even with both positive and negative infinity added as new elements, you will run into problems because your basic mathematical operations will not behave as expected.
@klossartig @SaySimonSay Die Frau hat natürlich recht, dass Veränderungen eher von denen ausgehen können, die in einer privilegierten Position sind. Ist aber in der Praxis schwierig. Ich mache mir keine Illusionen darüber, dass meine Einwände gegenüber Menschen, die sich im Gespräch sexistisch, rassistisch oder sonstwie abwertend oder spaltend geäußert haben, eine Veränderung in deren Verhalten bewirkt hat, auch wenn die Reaktionen meistens sehr einsichtsvoll erschienen.
@990000 Yes, that's the kind of plot you've been looking at. It's indeed instructive to sketch Bode plots by hand because that gives you a feel for how they relate to the transfer function. Not the most fun exercise but an important one for sure.
@990000 In the graph you can indirectly see the number of poles from the steepness of the rolloff. Additionally, you can see where the poles are located in the imaginary plane from the overall shape. The farther left the poles are in that plane, the more stable the filter (which amounts to less or no resonance from the synthesizer point of view). This diagram is usually called Pole Zero plot and that's a diagram where you can see the poles directly for what it's worth.
@990000 Poles are the zeros of the denominator of the Laplace transform of the transfer function. This graph is magnitude plotted against frequency, i.e. the amplification of the input signal for a given frequency. There are diagrams that explicitly show the poles and these are useful for exploring other properties when designing filters (in particular the resonance behavior in synth terms).
@990000 The term pole refers to the Laplace transform of the transfer function, the mathematical description of how a circuit reacts to an input signal. These are polynomial fractions and a pole is a zero (or root) of the polynomial in the denominator. If you graph the magnitude of this transform of the transfer function you get the graph you are used to (the frequency response). I guess, that's not very useful to you because it assumes knowledge of circuits, the Laplace transform etc.
@990000 The math behind that is not so easy, true. But perhaps someone might give you a hint or two if you were to mention what kind of an understanding you're looking for and roughly where you are stuck on the way there.