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"Veritasium" (YT) - "The Big Misconception About Electricity" ?

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adx:
One I needed to explain...


--- Quote from: bsfeechannel on March 25, 2022, 03:04:48 am ---
--- Quote from: adx on March 24, 2022, 02:26:38 pm ---This is all a bit silly - it started with a gentile troll about i vs j, then we're now back to arguments over half-arsed engineering.

--- End quote ---

You reduced engineers to mere solder monkeys (no Cartesian coordinates, no vectors, no y, no functions).



What do you expect?

--- End quote ---

Silliness? I was responding to "And of course we should remove the study of Cartesian coordinate system from electronics engineering because y doesn't appear on the screen of any oscilloscope ...". (Plus how did you find a monkey wearing Dave's T-shirt?)

But I thought I better explain what I mean by stuff like "Yes, stop studying Cartesian coordinates and silly unit vector formulas. Forget about y. Ignore "functions". Teach the oscilloscope display for what it is.".

It is a little story. I was suffering a non-authentic crisis of confidence wondering if my ignorance is more functional than I assumed, so when this appeared...


--- Quote from: SandyCox on February 12, 2022, 10:51:47 am ---https://archive.org/details/ThePhysicsOfVibrationsAndWavesH.J.Pain/page/n15/mode/2up

--- End quote ---

...I paged through it to check if it made sense. I even looked at some of the equations. Going "yep", "know it", "know that too".

Oh, can't find it, might have been a different reference. That kind of ruins my little story. Anyway, undeterred by it losing all context, it was something along the lines of the wave function operator with an omega t and x somewhere, and it said something like "this is valid for any function of x and t" - I stopped and thought "what function? itself? javascript?". A less erudite version of penfold's "whaaa?! a 1024-point DFT is just a 1024-dimension vector... with 1024 components... that represents the 1024-dimension signal vector... nooo, how can this be, it's frequency components!", in post number well lost that too after pasting it. It was there seconds ago.

Anyway it took me a few seconds to bend my brain around what that meant - by function they mean signal, waveform, shape, deflection of string, wiggles on scope. Not something to be 'solved' or 'refactored' or 'pondered in math101' or whatever the mathematicians do with equations. Yes, it's a concise description, but it doesn't represent what happens until you in effect solve it in your mind. It's kind of backwards. If engineering is applied physics and math, then you wouldn't expect an average engineer to work out bandgaps in a new semiconductor, so why the need for mathematical chops many won't understand and few will ever use in their entire careers? Many concepts in engineering are presented / taught / described in this overly abstract way - stuffy, boffiney, hard to access.

Of course you could say any engineer worth their salt should suck it up and learn to think like a mathematician - which is natural for some. But it's still obvious there is a divide between academia and what is used in the 'real' world, and one which by and large academia seems unaware of (or unwilling to accept). It reminds me of this type of mindset from 'experts':


--- Quote ---Exactly what is so complicated about:
   …
   x = ((PORTB & _BV(PB3) == _BV(PB3)); //x gets state of  bit 3

It's hardly the most complicated C ever is it?!?

--- End quote ---

... instead of x = PORTB.3 (which can be done in some other languages and nonstandard dialects of C). It is harder, it's not a fault of students or beginners that they find it so.

Yes, I'm not saying stop teaching the concepts of Cartesian coordinates of course (or erase all abstract mathematics) - but this implication that it's best for engineers to crowd round the textbook in candlelight to learn the ways of classical and renaissance mathematicians, is just too much. Claptrap (or perhaps Klaptrapp).

adx:

--- Quote from: penfold on March 27, 2022, 03:54:06 am ---
--- Quote from: adx on March 27, 2022, 01:06:24 am ---[...]
Why does the algebraic 'what if' solution to x^2+1=0 have direct mathematical relevance to phasors?

--- End quote ---

I had half-baked a response to that earlier actually (hopefully that doesn't get taken as evidence of non-causality), I was pondering my own initial reaction to complex numbers from high-school maths. I think that 'what if?' solution is typical of most people's first exposure to complex numbers, demonstrating that there are still "some roots" to an apparently 1d problem. I initially just accepted that it was 'nice' and plodded along.

--- End quote ---

I'm sure I remember you saying that in an earlier post - now I'm worried for causality!

I can't remember my reaction to complex numbers in high school - though I wrote a little story lastnight then wondered if it would be a good idea to post my tattered academic achievements. Can't do much more harm :).

I can't get completely past that what if. I (still) reluctantly accept bsfeechannel's "So it is clear that x is in another dimension." argument, which would seem to give complex numbers the genuine fundamental relevance to phasors that I sought.


--- Quote from: penfold on March 27, 2022, 03:54:06 am ---By about first or second year EEE maths, when functions of a complex variable were introduced formally with power series (of a complex variable), residues, etc, it shed a little more light on things, at least to demonstrate that the function of x, for which we'd only ever assumed to be a function of a real value (and yet had complex roots... go figure) could actually be a function of a complex 'z=x+jy' which more naturally has a complex root, where f(z)=z2+1 is now a surface plot with height defined for values of x and y... only the height is complex but only goes completely to zero at +j and -j (i.e. y=+1,-1). If you were to draw cross-sections of the surface plot (as x2+1 is the cross-section at y=0) and the same function will look slightly different... you can even plot a cross-section at an angle where both x and y are varying... or any arbitrary function that links x and y in response to an arbitrary parameter (I'm too tired to wonder if that was relevant... could be Euler's formula with 'phase' as a parameter... really not sure where I'm heading with that).

--- End quote ---

I'm yet to really work that out (or plot it in Octave), but as you say a function of a complex thing more naturally has a complex root. But when it comes to an extra dimension being generated out of 'nothing', it's drop anchor and haul back until I get to the what if place. Not that I think such a thing would be impossible (or icky), but because of that "despite the algebra of the square being the source of the number in the first place" chicken and egg situation (similar to the DNA argument a few posts back, where the machinery of its own encoding is needed to make it work). It's made of algebra (what if), so what if any modern impression of the 'reality' (particularly the neat 2D Cartesian uses) of imaginary numbers is no more than a product of our overactive imaginations? (Of course these uses would stay valid, but so would any arbitrary 2D system with the properties useful for phasors.)

If so, an illusion might in part be fostered by the implication of an orthogonal dimension by the x^2. The failure of that to solve if negative is a whole new dimension on top of that (for the output). Per bsfeechannel's words "x can be neither a positive nor a negative number, because such numbers give you a positive area. So it is clear that x is in another dimension." (which is for x rather than x^2, so I can see my argument doesn't really work). The area usually works for +ve x^2, then for -ve, something otherworldly happens to x and less so to the area. Or one of the dimensions (depending on the root) flips midway. Or it is real; squaring generates negative numbers (or the negation operator) from nothing in the same way I am complaining about about i. Then using those negative numbers (or really just the operator) and the same squaring operation, two imaginary roots are generated (or rotated into being).

Whatever the explanation (real or otherwise), a neat 2D phasor view does seem quite leapey faithey to me. Hence that anchor. Fortunately, I am not a mathematician, so it doesn't really matter.

I half had something about pole-zero responses and phase wrapping around, but better end that one there!

adx:

--- Quote from: HuronKing on March 28, 2022, 04:42:38 pm ---That difference is only in your mind - at least as far as us engineers are actually concerned.

--- End quote ---

I know - that is the basis of my argument about pedagogy. Otherwise I wouldn't care (and didn't for decades). I was going to say in response to SiliconWizard's idea about "what reality is" is that I think that I think therefore I am, therefore what I think is my reality. If that makes sense (which I'm hoping it doesn't, because you'd be doing better than me). Use me as a model of the most obtuse students, who may not understand a thing until it is rammed in directly. If I were a student now (odd mix of tenses) I would have feigned belief long ago. The use of a difficult to accept concept as a foundation pretty directly implies difficulty in accepting things that are built on it (either an unresolved struggle, or an unquestioning acceptance; the opposite of what we want science to be). It's really odd: We are saying to them that a number when multiplied by itself results in -1 is a 90 degree phase shift. Or if you want to understand a 90 degree phase shift, just 'work out' the square root of -1 and you'll be golden. It's mind-shatteringly difficult. Never mind the name, I think the hint given by the word "imaginary" is useful in learning to ignore it, and just use the rules. Anyway, I'm off on the wrong axis again.

I obviously don't know much about the history of vectors, even after reading that pdf, it might just be that I don't know what vectors are. I better leave that alone, after a quick look Wikipedia revealed no surprises.


--- Quote from: HuronKing on March 28, 2022, 04:42:38 pm ---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.

--- End quote ---

Ok, despite what I wrote above I am a lot closer to accepting that makes some sense: If I am going straight ahead, negative velocity might not be real for me at that moment but applying it will result in my distance units decreasing rather than increasing, so the 'mark' of what I will call "physical" numbers (positive reals) versus the imaginary nature of the negative numbers (because they are generated from those by a minus operator) has physical significance. In the same way, if I want to describe "sideways" as some unholy mix of positive and negative (or negative and positive), the lack of operator still points the way forward (as my reality, there is no delta to new freedoms like going in reverse). Similar for my FFT; the 'mark' of the real is how the DC component (oops I nearly said term) comes about, although positive or negative reals count and no DC offset need exist (which rains on my new parade a little). Still, if 180 degrees phase is produced by negation, then what's to say an extracorporeal mix of minus and positive can't produce all phases quantifiable? (Which is your point, I know.)

But "what's to say" isn't a proof. And we are clear in our claim that 90° = sqrt(-1), or rotation is "connected directly to solutions of x^2+1 = 0" - it's an extraordinary claim, unscientific in its boldness coming from historical ideas of something no one ever really worked out (to my knowledge). (In this sense perhaps mathematics is to engineering what the pre-science medicine is to modern medicine - full of ideas (many good) but isn't science?)

And generation of a whole new dimension? To the point where complex numbers are thought of as inherently "one number" while the same detail presented as an ordered pair is two (is a vector a number?). Forward / reverse is connected directly to solutions of x^2 = 1 as I mentioned lastnight. x^2 is effectively a statement of area which 'invokes' an extra dimension of our own making. Is it any surprise that doing strange things to that area can result in something which appears to have excess dimensionality? It could be fundamental, or it could be we set ourselves up for a trick and believe this illusion means more than it does.

And that's possibly all I need to say on it without knowing more. I have learned why complex numbers have fundamental physical relevance, but also why they might not.


--- Quote from: HuronKing on March 28, 2022, 04:42:38 pm ---
--- 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)

--- End quote ---

I didn't say they shouldn't learn multiplication. Just "if" addition works better. I gave the example (in a different reply) of measuring out a liquid rather than calculating the volume out. This is a practical result which just works better in many situations. Or a computer solution arrived at by filling pixels with colour then going over that counting them (say some sort of floor plan calculator). I also know some clients who would be frightened by multiplication (yes) and might not pay me if I went against their wishes and used 'complicated maths'. If wanting to put someone on the moon (then back here especially) it's probably better to replace both the consultant and client.

It's all abstraction anyway. I didn't bring up the example of not using multiplication, I just wanted to show how general the idea is (that it is always possible that the mathematics is too abstract).


--- Quote from: HuronKing on March 28, 2022, 04:42:38 pm ---Get... Descartes... out.... of... your...head... Why won't you listen to Gauss?

--- End quote ---

Bah, my answer to this part was to be a quote (I thought from Gauss) saying the true nature of the imaginary numbers remains elusive. Can't find it anywhere.

Anyway, you see from above why I think imaginary remains a good name. It stands as a warning that we (at least I) don't know for sure, and as humans we tend to get ideas into our heads and believe them without adequate evidence. I like to use qualified language in that case. I'm not saying Gauss was wrong, but I think there is a chance he was wrong.


--- Quote from: HuronKing on March 28, 2022, 04:42:38 pm ---And you straight up ignored the Keysight Impedance Measurement manual.

I give up.  :-BROKE

--- End quote ---

I looked at that, and saw "complex quantity" and "imaginary part" at the start. I had a bit of a laugh at "imaginary components" (always fun). Searching the pdf it does talk about complex and imaginary a fair bit in places, being 140 pages long and devoted to LCR measurement. I'm not suggesting that these terms don't appear anywhere reputable - I know full well what they mean in engineering.

For another example of absent imaginary, look at:

https://en.wikipedia.org/wiki/In-phase_and_quadrature_components
(I and Q suggested by TimFox on page 67 - I had half-penned a reply)

Not one mention of complex or imaginary.

I'm happier with that approach, but it doesn't mean I think complex phasors are "wrong" (they never stopped working), and now I understand sqrt(-1) better I might even begin to like the idea.

TimFox:
Yes, the voltages indicated as I and Q on a two-phase lock-in amplifier are "real values" in the common mathematical sense of the word.
However, when I use these values to calculate something useful, such as the frequency response of an amplifier or an impedance as a function of frequency, being of sound mind I do the simple complex algebra in Excel, setting the imaginary part of the voltage to "Q" and the real part of the voltage to "I".  Both values are functions of frequency going into the algebraic calculations.

HuronKing:

--- Quote from: adx on March 31, 2022, 03:16:16 pm ---But "what's to say" isn't a proof. And we are clear in our claim that 90° = sqrt(-1), or rotation is "connected directly to solutions of x^2+1 = 0" - it's an extraordinary claim, unscientific in its boldness coming from historical ideas of something no one ever really worked out (to my knowledge). (In this sense perhaps mathematics is to engineering what the pre-science medicine is to modern medicine - full of ideas (many good) but isn't science?)
--- End quote ---

Gauss and others worked it all out for us. In fact, some of the most brilliant minds in human history turned their attention towards this. It's the basis of the Fundamental Theorem of Algebra. It's not so mysterious, really.


--- Quote ---It could be fundamental, or it could be we set ourselves up for a trick and believe this illusion means more than it does.
--- End quote ---

I'm content that it's not an illusion since the mathematics has tremendous predictive power in physics and engineering.


--- Quote ---And that's possibly all I need to say on it without knowing more. I have learned why complex numbers have fundamental physical relevance, but also why they might not.
--- End quote ---

This is progress.  :D


--- Quote ---Bah, my answer to this part was to be a quote (I thought from Gauss) saying the true nature of the imaginary numbers remains elusive. Can't find it anywhere.
--- End quote ---

You're probably referring to the 'shadow of shadows' quote which should be weighted in its context. Gauss was tackling Euler's Identity in his doctoral dissertation to prove the Fundamental Theorem of Algebra.


--- Quote ---Anyway, you see from above why I think imaginary remains a good name. It stands as a warning that we (at least I) don't know for sure, and as humans we tend to get ideas into our heads and believe them without adequate evidence. I like to use qualified language in that case. I'm not saying Gauss was wrong, but I think there is a chance he was wrong.
--- End quote ---

As a teacher it is the WORST name to give it.

Me: "Okay class, now that we've learned about real numbers, let's now learn about imaginary numbers."
Student: "Wait, why are we learning fake math?"
Me: "No, it's real math."
Student: "But you said it's imaginary."
Me: "Not really, the better name is complex numbers."
Student: "Oh God no! Why do we need to learn complicated math?"
Me: "It's not complicated. It's complex."
Student: "Yea! That's what I said. Math is stupid. You're making me learn complex imaginary math that I'll never use. Blegh."

There is nothing qualified about the language calling it 'imaginary.' It is straight up just repeating Descartes' lack of, heh, imagination in foreseeing where numbers in the complex plane could be used for helping humanity. Our understanding of complex numbers has advanced significantly since Descartes.
If I can make an analogy, we don't call particles of light "corpuscles" even though Newton conceived of the first particle-models of light. We call them photons, because calling them corpuscles would carry with it a lot of baggage from Newton's other arcane ideas.

Earlier someone mentioned that being mad about the 'imaginary' convention is like being mad about our plus-minus red/black current convention. I soft disagree with that. No one has any trouble learning electricity with the historical convention, the math all works out the same, and a simple sign reversal is all that's required to talk about the direction of charge flow for current.

Whereas students think there is something actually meaningful about the name 'imaginary' number. Or even, as you're suggesting, that there is a chance Gauss was wrong. There isn't - at least in as much as ANY portion of mathematics has meaning.


--- Quote ---For another example of absent imaginary, look at:

https://en.wikipedia.org/wiki/In-phase_and_quadrature_components
(I and Q suggested by TimFox on page 67 - I had half-penned a reply)

Not one mention of complex or imaginary.
--- End quote ---

Lulz - the suggested additional reading is Charles Steinmetz' Theory and Calculation of Electrical Apparatus where that icky j appears on page 2:
https://www.google.com/books/edition/Theory_and_Calculations_of_Electrical_Ap/UjEKAAAAIAAJ?hl=en&gbpv=0

Maybe take your investigations beyond Wikipedia?  ::)
https://www.dsprelated.com/showarticle/192.php

I'm amused by this site also taking the great pains to explain how the j is unfortunately named and glossed over too quickly when it is taught. In any case, You can thank Euler for making sines and cosines equivalent to j rotations.


--- Quote ---I'm happier with that approach, but it doesn't mean I think complex phasors are "wrong" (they never stopped working), and now I understand sqrt(-1) better I might even begin to like the idea.

--- End quote ---

If you want to clunk around with sines and cosines you can - and sometimes its better. Other times it isn't. Being comfortable with both makes you a better engineer.

When I used to be a private tutor, I always told my students that mathematics is like long hair.
You can wear it up.
You can wear it down.
You can color it.
You can cut it... and it'll grow back.
You can part it in the middle, on the side, wear it as bangs, or tie it into pigtails and ponytails.

But at the end of the day... it's the same hair, just dressed up differently.

And some social occasions require the hair to look a certain way. And sometimes the way it looks doesn't matter - but it's function matters (like putting the hair up so its out of the way). And other times the way it looks is ALL that matters regardless of how impractical it is.

Sometimes, someone comes along with a new way of styling hair. Maybe that styling method sucks or looks really ugly... until fashion changes or you find a really good reason to do hair that way.

If you're a hair stylist, you can be a boring technician who only knows 3 haircuts and 3 ways to comb hair. And you can have a perfectly successful career as a stylist. But that's all you'll ever be capable of doing.
Or, you can be a stylist who embraces new fashions, learns new ways of constructing and deconstructing the hair with the tools of the trade (scissors, clippers, steamers, gels, dyes, shampoos, etc etc). You'll then be sought out for your talents at solving any kind of hair problem and get paid lots of money to do it. And you might even find that emotionally fulfilling.

Or all of that is too hard and that's not the kind of work you want to do. You don't care about getting girls ready for prom or dressing hair for weddings. You're satisfied giving buzzcuts to marines. That's fine and admirable and, yes, you don't need to know anything about curling hair to do the buzz-cutting job.

But thank goodness there are skilled stylists who can make a young lady's dreams come true with a gorgeous effortless looking hairdo.  :-*

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