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| "Veritasium" (YT) - "The Big Misconception About Electricity" ? |
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| adx:
--- Quote from: bsfeechannel on March 27, 2022, 04:55:11 pm --- --- Quote from: adx on March 27, 2022, 03:01:41 am ---The question then remains whether this fundamental nature of the number (and complex plane) has direct relevance to phase of sine waves, or whether phasor analysis merely purloins the property of the complex plane as a "handy trick"? --- End quote --- If it is only a "handy trick", it is already useful and worthy of our attention as engineers. We want shortcuts to solutions for our engineering problems. --- End quote --- I don't think I suggested any different, except maybe the notation is confusing. It's just that we are taught something that turned out not to be necessary or relevant, in a sense. Complex numbers are an interesting story, but not knowing what sqrt(-1) 'is', trips me up if I'm told "it is completely fundamental" rather than "based on a true story of i, but events or characters might have changed, so don't fret" - instead I am left to myself to work out that mathematics is better ignored in engineering. That's about where I put a :-//. --- Quote from: bsfeechannel on March 27, 2022, 04:55:11 pm --- --- Quote from: adx on March 27, 2022, 01:48:48 pm ---Yes, if it "adds" nothing practical or needs to be applied abstractly by some engineers who might then not know what they are doing as clearly. --- End quote --- Of course it adds practicality, otherwise it wouldn't be taught. Not only that, it adds insight, which is essential for engineering. --- End quote --- Not for everyone it doesn't. I wasn't describing a theory of mind, but a reality of minds and situations. There are people and situations for which multiplication might not work for them as well as addition, and might result in much less understanding. Addition might even be more practical in a computer, some sort of realtime situation. Ok so maybe these people are not cut out to be engineers, but there are much more advanced mathematical topics in engineering that are even more optional (as the power triangle example above shows). I'm not suggesting it isn't taught, just that it can't be assumed to be useful. I think Maxwell's equations succumb to the same problem, of looking too 'theoretical and optional', when they are not (the concepts are fundamental, even if the analytical solutions are too much for many engineers to really get). Mathematical models as-taught for engineering added mess and confusion, not insight for me. You could assume that makes me completely stupid. I could be pretentious and say all engineering (and physics) concepts are simple to me and I find the math a distraction. With the reality somewhere within that space. For all the millions of engineers now in the world, there have to be some differences between them. --- Quote from: bsfeechannel on March 27, 2022, 04:55:11 pm ---Because you don't have to work with AC circuits, filters, control systems, or RF, and you see no use for it in your daily tasks, it doesn't mean that mathematical concepts like complex numbers should be abolished from engineering. For working with ADCs, for example, a different set of theorems and math tricks are required. I could conversely say that the Nyquist theorem is a waste of time, if I my job as an engineer didn't involve sampling analog signals. Or that the Viterbi algorithm, without which CDMA, GSM, WiFi, speech recognition and a whole bunch of other technologies wouldn't be possible, that I had to study while in engineering college, is rubbish if my job as engineer had nothing to do with telecom. --- End quote --- I do work with AC circuits, filters, control systems, even RF. Most of it has become unavoidably cookie-cutter or specialised because of chips and advances in technology. About the only thing which uses as-taught maths of those is analogue filters, where even for me the cookie-cutter solutions do not always, well, cut it. You've seen the power triangle reference, and can see how complex numbers could be optional, so why are they needed? Tradition? I guess I am saying abolish it, but I know it wouldn't be practical because it is such a strong tradition, and I know it is at least partly motivated by my prejudice against mathematical notation in engineering, which I know not everybody shares. The Nyquist sampling theorem is easy to describe in words and see why in a simulation (perhaps in Excel, to impress what I mean there), so isn't the kind of thing I'd want to say is a waste of time. It's more the pages of mathematical descriptions which I can only assume professors must know half their students don't even begin to comprehend properly. Then there's stuff I think is outright misleading, like there being complex numbers in an FFT - real values (again Hermitian) go in, so in the output why do the sines get a j while the coss get nothing, when (despite complaints) imaginary numbers are very different in character from reals and there is nothing like reactance in the phasor to even suggest some imaginaryness (despite complaints) to one of the axes? j definitely has a supposed meaning as one of the roots of x^2=-1 (and how do we know the one we pick as positive is the -+ one or the +- one?), 1 is a natural number with a clear positive. I don't think I would ever call it "rubbish" though, it's a minor annoyance. But to fresh students with a weakness (or perhaps a strength) in maths, it can be extremely (and I have to assume unnecessarily) confusing. Anyway, I can't see the point in getting too worked up over (or taking too seriously) theory and learning at university. Your mention of Viterbi decoding reminded me of a seminar thing (with sausages) I went to recently (10 years ago!) about LTE and one of the presentations went right over my head with words like "Bayesian" this and that. A quick search for that now turns up things like: --- Quote ---... The coexistence problem is modeled as a decentralized partially-observable Markov decision process (Dec-POMDP) and Bayesian inference is adopted for policy learning with nonparametric prior to accommodate the uncertainty of policy for different agents. A fairness measure is introduced in the reward function to encourage fair sharing between agents. Variational inference for posterior model approximation is considered to make the algorithm computationally efficient. ... --- End quote --- Students need to choose their poison and pick their battles. Oh noes, too long again, I meant to reply to other stuff. |
| HuronKing:
Back now after a weekend trip. A few comments. --- Quote from: adx on March 27, 2022, 01:48:48 pm ---Only time for a partial reply for now: --- Quote from: HuronKing on March 25, 2022, 07:20:57 pm --- --- Quote from: adx on March 25, 2022, 04:04:02 pm ---First, my concern over sqrt(-1) in electrical engineering, penfold has it right: "and the j is an operator rather than a quantity ... it is stretching it a bit far to say that it is a physical quantity". --- End quote --- Did I say it was a physical quantity? Please show me (I've tried to find where I might've implied that but I don't see it). j is not an Ohm. But it is a representation of phase-shift in Ohms and a damn good one. Is that not physically relevant? --- End quote --- Tricky semantics. What I and I assume penfold were referring to was somewhere between a physical unit and representation as a tool. You said sqrt(-1) "has immense physical significance, just as 'zero' and 'negative' have immense physical significance" which I took to be that middle meaning. Saying j is physically relevant is different from saying sqrt(-1) is, to me. The latter being a very abstract mathematical concept, but j being defined as a practical tool by Steinmetz (yes, with overlap). sqrt(-1) is the first whole positive imaginary number (if there is such a thing) hence a quantity (of sorts), j is a rotation operator as defined by SandyCox in (a, b)(c, d) = (ac-bd, ad+bc) (with j as b or d). They happen to be algebraically identical. --- End quote --- That difference is only in your mind - at least as far as us engineers are actually concerned. For example, the vector is an abstract mathematical concept. In fact, no one thought they were very useful or had much relevance until Heaviside showed the world what it could do (remember the 4 equations of Maxwell are really the Maxwell-Heaviside Equations). Seriously, Heaviside had to FIGHT to get vectors accepted. I recommend you read The History of Vector Analysis. Here is a short timeline synopsis of the book but the book itself is loaded with a colorful stories of what seems so 'obvious' to us [simple vectors] had to be hard-won: http://worrydream.com/refs/Crowe-HistoryOfVectorAnalysis.pdf But here we are using vectors all the time. A vector has magnitude AND direction... and that direction property necessarily is subject to a property of rotation (because I need a reference direction for the concept of 'direction' to even make sense), which is connected directly to solutions of x^2+1 = 0. There is no coincidence that Heaviside vectorizing electromagnetism led Steinmetz to the realization that complex analysis of phasors is another, much simpler, way of solving power problems. I don't care about Descartes' idiotic 'imaginary' and 'real' naming convention that we've chosen to stick with. He never solved a circuit. :rant: --- Quote from: HuronKing on March 25, 2022, 07:20:57 pm --- --- Quote ---I don't think it is any sort of tautology to say mathematical concepts are not real, if one then goes on and asserts that some part has physical relevance. Not all engineers are naturals at maths and can easily identify where that link appears (ie goes from nothing to something without explanation). Some people here seem to be struggling with it too - perhaps from over-familiarity. --- End quote --- You might as well be arguing that multiplication has no 'physical relevance' to engineering because you could just add the numbers up... like, yes? What is your point? Should we count on our fingers and toes because applying math makes us feel dumb? ;) --- End quote --- --- Quote ---Yes, if it "adds" nothing practical or needs to be applied abstractly by some engineers who might then not know what they are doing as clearly. --- End quote --- Such an engineer wouldn't even know how to apply the abstraction. Honestly, they need to 'git gud.' If not, those engineers should be replaced with engineers who can solve it using the abstractions. I've provided copious amounts of examples of problems that were incredibly difficult or even sometimes completely inscrutable to solve without complex phasor analysis. If someone wants to solve 100x100 by adding up 100 100 times... their billable hours will be higher than mine who can solve it in 2 seconds with my 'handy trick too-hard abstraction.' I know who the employer is going to hire. ::) And if such an engineer is never going to apply to solve big addition problems that need multiplication because the abstraction is too hard... fine. Good for them. But they'll never land a man on the Moon counting on their fingers and toes. 8) --- Quote ---For something like sqrt(-1), I don't know where it gets real. --- End quote --- Get... Descartes... out.... of... your...head... Why won't you listen to Gauss? --- Quote --- --- Quote from: HuronKing on March 25, 2022, 07:20:57 pm ---I'm not citing waffle-y texts at you. I'm citing actual engineering practices. You can take them or leave them. https://www.electronics-tutorials.ws/accircuits/power-triangle.html --- End quote --- Although I've clarified more since, this is exactly what I don't have a problem with. j is defined only in the annotations on the diagrams as a 90 degree shift pictorially and as reactance. j doesn't appear in any of the body text or its formulae. The only hint as to what j might be (as a symbol) is mention of "which is the vector sum of the resistance and reactance". This is what I mean by things like "to the point they realise sqrt(-1) has no physical relevance, with j being the unit vector that I say it is". --- End quote --- And you straight up ignored the Keysight Impedance Measurement manual. I give up. :-BROKE I'm sticking this series here again just because: |
| bpiphany:
In this, of all threads, we can of course not miss pushing this video =D |
| SiliconWizard:
I also mentioned epsilon numbers, and for something "closer" to complex numbers, you have dual numbers. https://en.wikipedia.org/wiki/Dual_number Another "handy trick". Now the question remains. What really makes "real numbers" more real than complex numbers? Are rational numbers more real than irrational numbers? Are transcendental numbers less real? Or are they just a handy trick? Is infinity in R the same as infinity in N? Is infinity even "real"? Do you think dual numbers are less real than complex numbers? Is there some kind of hierarchy of reality that makes sense outside of just being another handy trick? |
| TimFox:
A mathematical approach or method applied to engineering is only "not real" if it predicts results that do not agree with practical outcomes, like the frequency response of an RIAA R-C network measured with simple equipment. |
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