Arent they a way to describe phase; that leading and lagging stuff? A fellow in my last at-work group described making a zero dissipation speed reducer for a fan by using a capacitor. It shifted the phase of the current, relative to the voltage on the AC line. Current there but voltage not yet? You wont get the same power as when the two are better sync'd. "j" or "i" being somewhere in that reality mathematically.
Yes, at one frequency. In phasor analysis you can use polar coordinates where phase is an angle, or rectangular coordinates (which are complex numbers) to represent the same point.
Don't make me quote George Box. Us humans do not have infinite resolution and perfect precision. Models are fundamentally approximations that are more than enough to surpass our senses.
Last edited:
Okay. What are the numbers that describe the limits of our senses? Where is the line for each sense and how is it defined?
Ouch! It's Friday night, I don't think I have enough left to give this question a proper answer.
As far as hearing is concerned, you can certainly take the Nyquist–Shannon theorem, add 50% of extra margin and say it's a definite boundary.
For noise and distortion, anything below -120 dB is certainly safe to ignore.
Frequency perception, 20 Hz to 20 kHz are still good boundaries for the most gifted among us. In my case, it's more 40 Hz - 13 kHz at this point, and I am only middle-aged.
Is there scientific evidence in support of that particular number as the exact line, or is it a fuzzy quantity? Maybe there isn't an exact number because it would depend on the exact time-domain distortion waveform and maybe its crest factor, which is undefined? Why not say -130dB is certainly good enough? Where does the exact number -120dB come from?
Pi is exact (mathematically its an exact ratio, and and exact point on a number line), not fuzzy. Its just not a member of the set of rational numbers.
Are you saying that capacitors don't have things like tolerances and voltage coefficients? You do a calculation get an exact number, but a physical capacitor does not have perfectly LTI capacitance. So your calculation is approximate in relation to the physical reality.
Complex numbers identify phase, as well as the resistive and reactive components of impedance.
"Zero dissipation" speed reducers for fan motors are nothing new. Phase correction of motors ( a big thing with big motors) greatly improves electric motor efficiency.
You could say the same about resistors.
Your objection in no way, shape, or form casts shade on complex numbers and their usefulness. It's true but a total non-sequitur
And I do.
I haven't said anything critical about mathematical modeling to get close approximations. What I have said is that an idealized mathematical model, close as it may be, is not exactly the same thing as the physical reality being modeled.
Its like this: Math is a set of rules and symbols invented by man. The universe was not invented by man and is not limited by his logical constructs. Its the universe that is fuzzy, not man's mathematical logic. I don't see why that is so hard to understand.
That number is a massive overshoot.
Numbers have been researched using empirical studies, but mathematics cannot help us with that.
Yet, even though we may not know how far a human can throw a ball, it's safe to say it's below 100 miles. So, you can use such exaggerated boundary lines to realize we are already measuring things that do not matter.
Example: Worrying about noise or distortion 120 dB below the level of a reference tone; which is like worrying about the possible existence of human beings who could throw a ball farther than 100 miles away.
Saying "everything is fuzzy" does not mean "we know nothing" or "everything is possible".
In practice, it depends on many factors, including individuals, but again this doesn't imply there is a living human on earth who can hear a pin drop in Tokyo while drinking coffee in San Francisco:
https://www.axiomaudio.com/blog/distortion/
Pi, the concept, is exact. But any numerical representation of Pi is approximate. This is the duality that made me refer to it while answering your question.
Agreed.
BTW, thresholds of audibility, the numbers we have that describe what people can hear are not exact. They are fuzzy because they are estimates of an average for a population (estimates of the middle of a bell curve). Also, the most accurate statistical models of distributions describing what people can hear are not necessarily Gaussian bell curves. Thus so-called outliers may not be all that rare.
- Status
- Not open for further replies.