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

[SiliconWizard]

If you go on arbitrarily adding parameters and degrees of freedom, you end up with the box set of Star Wars, and calling that a quantity.

Actually, reducing the degrees of freedom to just 1 *is* the arbitrary approach here. The universe doesn't care about our 1-dimensional constructs. It's just a useful (for us humans) abstraction as any other.

As to "quantity", what is your definition?
For complex numbers, I guess the closest to what we are used to when talking about quantities is to consider their polar form. The module and argument of a complex number are quantities that may be easier to grasp.

[adx]

Oh noes. Looks like I'm going to have to continue. There are unlikely to be any solutions beyond this point.

[adx]

If you go on arbitrarily adding parameters and degrees of freedom, you end up with the box set of Star Wars, and calling that a quantity.

Actually, reducing the degrees of freedom to just 1 *is* the arbitrary approach here. The universe doesn't care about our 1-dimensional constructs. It's just a useful (for us humans) abstraction as any other.

As to "quantity", what is your definition?
For complex numbers, I guess the closest to what we are used to when talking about quantities is to consider their polar form. The module and argument of a complex number are quantities that may be easier to grasp.

How is any of that different from my point?

By quantity I mean "how much" or "how many", subtle variations possible but same general meaning. Polar form is two quantities.

[adx]

18th and 19th century mathematics is something that happened to other people.

It would appear so. I'm starting to wonder if any modern engineering requires that sort of mathematics. Engineers don't tend to use it directly that often, some not at all. Basic arithmetic on a computer seems to be enough for the 21st century. So "other people" might be 20th century engineers.

(I know that wasn't your point, but it is what springs to mind.)

[adx]

Well I guess I just don't believe. If someone like me insists on being an ignoramus who won't or can't understand (I can't be expected to tell the difference), and you are limited to 'appeal to authority adjacent' claims because there is no trivial proof, then in the absence of launching into full time study I can just remain skeptical. It's not a carload of students trying to get to the top of a hill (then not drive off it). I can still use I and Q, and I can pretend j doesn't mean anything beyond how it gets used.

Again, I never appeal to authority. I've provided ample resources to read from Steinmetz and Clarke down to YouTube level basic introductions. You've got the full gambit of resources at all levels of rigor available. Something something horse to water.

I should have left it "no proof trivial enough to satisfy me", it seems when justifiably hindered by that situation you will resort to an appeal to authority:

Complex numbers, as much as reals, and perhaps even more, find a unity with nature that is truly remarkable. It is as though Nature herself is as impressed by the scope and consistency of the complex-number system as we are ourselves, and has entrusted to these numbers the precise operations of her world at its minutest scales."

— R. Penrose

I don't blame you, but that's no longer "adjacent".

My "ignoramus" premise might not be true however. I have looked through both Steinmetz and Clarke better (can't read them all right now) and have not found enough to satisfy me that complex numbers are innately physical (or whatever). Steinmetz does use them to solve a non-phasor (transient) equation which has complex roots (damped oscillation), but he is then at great pains to say they should produce a real result - closer, but an artefact of using algebra to do calculations. Clarke is likewise careful to ensure there is no overly strong buy-in to a mathematical concept of complex numbers, and she treats vectors and complex quantities (being a complex of two quantities) almost as equivalent. Both authors use it as a tool at a time when analytical solutions were an enormous optimisation.

The question is whether imaginary numbers deserve to be "an axis", or just happen to work that way because we think they should. Imaginary numbers are dreamed up from fanciful mathematical impossibilities (x^2 is non-physical for -ve x: we can't have negative length).

You have 3 apples, and want to take away 5 apples. So you have negative 2 apples.

NEGATIVE 2 APPLES? WHAT IS THIS SORCERY? This is just mathematical claptrap invented to compensate for made up problems and invent solutions.

How can you have negative apples? IMPOSSIBLE!!!! 

These excuses make you sound like a pre-medieval mathematician.

That is the look I am going for.

Hardly dents my argument (or really evidence) that some references and areas of engineering use phasors without sqrt(-1), or even j. I'm not saying j isn't widely used.

How is that even an 'argument' to have? Like, yes? What is even the point of what you're trying to say now?

Not now, then. Twice I provided (well you did for one) examples of the concept not being used or necessary, both times you were up on my case trying to argue around the facts. The piece I left off that comment (again to try to make it shorter probably errantly) was "You don't need to try to prove it is." -  you're grasping at straws, I would have thought needlessly.

[adx]

[in response to penfold]

I'm frustrated that after pages and pages of conversation on this point we return RIGHT BACK TO SQUARE ONE. ...

That's because there seems to be no solution but you believe there is.

I'm going to have another chomp at this cherry:

So, if I can assign a forwards and backwards direction to a quantity (positive and negative)... why is it 'OMGZ IMPOSSIBLE MAN!' to assign... rotational direction to the quantity? Rotation isn't just forwards and backwards, but all the places in between. That's all sqrt(-1) means. I know you know that - but after many replies and seeing adx's latest comment (where he asks yet again what the point is of sqrt[-1]) I just shrug now. 

So now I know that you do think sqrt(-1) is a fundamental property of all numbers, I can understand it (and your subsequent reply) in context. Negation is no more than a 180 degree rotation, half the complex nature that all numbers possess, with the other half ready should it be needed. That's a matter of belief. One I don't seem to share, due to insufficient evidence. I don't think it's impossible or implausible or even something I should believe against. It's just that when faced with fanciful notions like "how many sheep do you have" -> "oh, about 34 + j0", I am entitled to remain skeptical. Perfectly entitled.

[HuronKing]

I'm being called back in:

I should have left it "no proof trivial enough to satisfy me", it seems when justifiably hindered by that situation you will resort to an appeal to authority.

Look man, math is hard. I'm not writing a math textbook in a forum post to 'satisfy you'. I've linked you to videos and articles (including super-intro level videos) for you to get educated on the proofs and the history behind those proofs. It's not appeal to authority. I am not saying 'so and so said so so therefore it's right.' I'm saying there are copious resources at many levels of competency to build up your knowledge. Here is yet another one:


If you're too lazy to try or you have a cognitive/religious resistance to it (see my remarks below) - that's on you. I'm only going to spoonfeed you so much.

Steinmetz does use them to solve a non-phasor (transient) equation which has complex roots (damped oscillation), but he is then at great pains to say they should produce a real result - closer, but an artefact of using algebra to do calculations. Clarke is likewise careful to ensure there is no overly strong buy-in to a mathematical concept of complex numbers, and she treats vectors and complex quantities (being a complex of two quantities) almost as equivalent. Both authors use it as a tool at a time when analytical solutions were an enormous optimisation.

Translation:
"Steinmetz and Clarke use them to solve physical problems but I'm not convinced those numbers have physical meaning."

Whatever dude.

That is the look I am going for.

Wait, are you saying you want to raise pre-medieval mathematical concepts that were summarily rejected in the last 200 years?

Gawd, 18th and 19th century mathematics really is something that happened to other people.

Not now, then. Twice I provided (well you did for one) examples of the concept not being used or necessary, both times you were up on my case trying to argue around the facts. The piece I left off that comment (again to try to make it shorter probably errantly) was "You don't need to try to prove it is." -  you're grasping at straws, I would have thought needlessly.

Because whatever you're trying to argue on this point is stupid whataboutism. Arguing about places where complex numbers are not necessary to solve the problem is utterly immaterial to complex numbers themselves or what they are used for. It's a ridiculous tangent.

That's because there seems to be no solution but you believe there is.

 

So now I know that you do think sqrt(-1) is a fundamental property of all numbers, I can understand it (and your subsequent reply) in context. Negation is no more than a 180 degree rotation, half the complex nature that all numbers possess, with the other half ready should it be needed. That's a matter of belief.

And with one fell swoop you have reduced mathematics in engineering and physics to a matter of religion.

I guess Paul Dirac spoke a magical spell and willed positrons into existence with complex numbers. 

One I don't seem to share, due to insufficient evidence. I don't think it's impossible or implausible or even something I should believe against. It's just that when faced with fanciful notions like "how many sheep do you have" -> "oh, about 34 + j0", I am entitled to remain skeptical. Perfectly entitled.

And there we have it - the extent of your mathematical desire is counting sheep on your fingers and toes. Are you a shepherd or an electrical engineer? 

I've said over and over and OVER again that not everyone needs the complex numbers to solve their equations nor does every equation necessitate writing the complex form (even if it is always there, hiding, lurking, waiting to pounce on you!  ).

However, voltages, currents, and power are not sheep... and your conflation of voltage, current and power with sheep in an electrical engineering forum is deeply disturbing.

The definition of power is S = VI* = P + jQ VA. That's a complex number. Whine about it all you want - that's how it is. And that's the simplest form of it - it gets worse with unbalanced systems or non-linear systems. 
https://en.wikipedia.org/wiki/AC_power

What you are NOT entitled to is to tell other engineers they don't require complex numbers as you do here:

I'm starting to wonder if any modern engineering requires that sort of mathematics. Engineers don't tend to use it directly that often, some not at all. Basic arithmetic on a computer seems to be enough for the 21st century. So "other people" might be 20th century engineers.

I literally told you, as one example, that you can't even use HFSS Antenna E&M Simulation Software without inputting variables in terms of complex numbers. Did you forget? It was a bunch of pages ago, here it is (p.12 for example):
http://www.ece.uprm.edu/~rafaelr/inel6068/HFSS/HFSS_Antenna_v2015_v1/workshop_instructions_trainee/ANSYS_HFSS_Antenna_W03_1_Post_Processing.pdf

This is an entire field of engineering whose automated software cannot even be used without a deep understanding of complex numbers to even input the values for calculation. Have you ever even heard of an S-parameter?
https://en.wikipedia.org/wiki/Scattering_parameters

I've never used this software but sure seems like a good understanding of complex numbers is would be handy here, especially for Optimal Power Flow Analysis (given that you need to know what the kVAR and VA units all mean in the various fields):
https://etap.com/docs/default-source/qa-documentation/etap-getting-started.pdf

It's funny to me how hand-wavy you are about "oh computers will do it all" when the computer simulation is only as smart as the engineer who uses it. Garbage in, garbage out, as they say. 

PS
I want to reiterate, as I said pages ago, I'm not terribly interested in metaphysical questions like "does mathematics physically exist." That's a question for philosophers.

What I am interested in, from the question posed pages and pages ago, is can these numbers be assigned physical meaning for solving actual problems. I've never seen the number "3" so arguing about whether it exists or not is pointless here - let alone arguing whether sqrt(-1) exists...

But I have seen 3 apples and I have seen complex power. And if our descriptions of those phenomena be but an illusion, they are a damned good illusion, because somehow the illusion has predictive power for revealing phenomena we've never seen before. That makes it fantastically relevant and physical.

[penfold]

[in response to penfold]

I'm frustrated that after pages and pages of conversation on this point we return RIGHT BACK TO SQUARE ONE. ...

That's because there seems to be no solution but you believe there is.
[...]

One thing for which there is one true answer, I do know for sure is that aether is most definitely real... it's what makes varnishing in enclosed spaces so much fun.

[bsfeechannel]

Engineers don't tend to use it directly that often, some not at all.

Engineers you know. Tifify.

To me, complex numbers are second nature.

Basic arithmetic on a computer seems to be enough for the 21st century.

You probably don't know what the fx button on a spreadsheet does.

So "other people" might be 20th century engineers.

The 21st century engineer is inexcusable about his ignorance of math and physics, because knowledge has never been so accessible.

[TimFox]

"Twice I provided (well you did for one) examples of the concept not being used or necessary."

Yes, also the concept of Bessel functions is not needed when I balance my checkbook, but they are quite useful in calculating the harmonic content of a transistor collector current (driven by a small sinusoidal base-emitter voltage).
Yet another piece of 19th century mathematics that is irrelevant to one or even three applications. 
However, the basic concepts of logic disagree with your argument here, and they continue to be relevant to digital design.
I retired early in the 21st century, which is now only 22 years old, so I didn't work with any engineers born in the current century, but electronic engineers with whom I worked into this century (including hardware design and image-processing computation engineers) found many practical uses for complex numbers in their work. 
I posted somewhere an anecdote where one of those hardware engineers doing some calculations complained to me (in jest) that Excel couldn't handle complex numbers and I replied (also in jest) that Excel was designed by accountants who would go to jail if they used imaginary numbers.

[hamster_nz]

I posted somewhere an anecdote where one of those hardware engineers doing some calculations complained to me (in jest) that Excel couldn't handle complex numbers and I replied (also in jest) that Excel was designed by accountants who would go to jail if they used imaginary numbers.

 

[adx]

Well that went a lot better than I thought it was going to.

He he. All that from saying "I don't believe". Religion and metaphysics eh?

Probing the extents of human belief is tricky, but interesting. I'm quite proud of what I have achieved. Being right is only the icing on the cake.

Ok I'll wear it as a fair characterisation, excepting some inaccuracy and missing of the point.

I'll reply to a few points here and there, in a less 'aconventional' way . Maybe.

[bsfeechannel]

He he. All that from saying "I don't believe". Religion and metaphysics eh?

Not believing in certain things is also part of any religion.

I'll reply to a few points here and there, in a less 'aconventional' way

Yes, show us more how your belief in the power of ignorance can help engineering in the 21st century.

We're interested.

[SilverSolder]

[...] the power of ignorance [...]

Sometimes I feel as if it is the most powerful force in the Universe....

[adx]

[...] the power of ignorance [...]

Sometimes I feel as if it is the most powerful force in the Universe....

You beat me to it. I was going to say an area of research close to my heart (well, not really) is artificial stupidity - only with AS can one capture the true and it turns out most common range of human behaviours (and other animals, but the force is strong in humans - it's all that brain, most humans don't use much most of the time, but it's got to be doing something). One day perhaps I could be the model organism for the AS machine clone. Unlikely I know, but I like to live my life as if it could happen. It doesn't always come naturally to me - I've got to try harder than many, but I think I am doing quite well these days.

[penfold]

Ignorance is however very powerful when used well, nobody progressed any greater understanding by reading a textbook and being satisfied with the answer. Ignorance in others is also very revealing of a teacher's abilities and often demonstrates weaknesses in the pedagogical representation of concepts.

[TimFox]

Ignorance is the human condition.  None of us can possibly know everything.
Stupidity, however, is being proud of one's ignorance.

[bsfeechannel]

Ignorance is the human condition.  None of us can possibly know everything.
Stupidity, however, is being proud of one's ignorance.

Neither ignorance nor stupidity have been of any help to engineering.

[TimFox]

Ignorance is the human condition.  None of us can possibly know everything.
Stupidity, however, is being proud of one's ignorance.

Neither ignorance nor stupidity have been of any help to engineering.

That's right, but we can avoid stupidity.

[penfold]

Ignorance is the human condition.  None of us can possibly know everything.
Stupidity, however, is being proud of one's ignorance.

Neither ignorance nor stupidity have been of any help to engineering.

That's right, but we can avoid stupidity.

Not disputing the fact, maybe the sentiment. A "lack of ignorance", or at least "the assumption of the correctness of one's own knowledge" is my core problem with most engineers, they bound forth into a problem with some assumption of how to solve it, and when questioned why they chose that approach, all too often do I hear "oh, it's like such a problem"... when it's not. They just seem to think that the human brain is just some endless store of historic knowledge and they struggle to rationalize a more "proper" solution. Just a side rant, I'm sure it's descriptive of nobody here, but sometimes ignorance is good, a little knowledge can too easily mask a lack of intelligence.

[TimFox]

I find it important to be aware of ones own ignorance, and therefore attempt to learn more when faced with a novel situation.

[bsfeechannel]

That's right, but we can avoid stupidity.

And I would add that the ignorant engineer is a liability. The stupid engineer, a menace.

Ignorance is however very powerful when used well, nobody progressed any greater understanding by reading a textbook and being satisfied with the answer. Ignorance in others is also very revealing of a teacher's abilities and often demonstrates weaknesses in the pedagogical representation of concepts.

The teacher is not the culprit if the student doesn't want to learn. In the specific case of the use of complex numbers in engineering, there's nothing more pedagogical than Steinmetz paper entitled "Complex Quantities And Their Use in Electrical Engineer". The explanation is so clear that any high-schooler can understand. At least I and my colleagues did at the time. And if you want to ascribe any physical significance to the complex numbers, just look around you. The ubiquitous and affordable distribution of energy wouldn't be possible without the help of its application to engineering. But If you want to go down the rabbit hole of the meaning of numbers, whatever numbers, just start asking what is so two about two that makes it a two and not a three, or a four? That has nothing to do with engineering itself. And if you don't know how to answer those questions, you cannot possibly advocate for the eradication of the use of the number two from engineering.

[penfold]

Ignorance is however very powerful when used well, nobody progressed any greater understanding by reading a textbook and being satisfied with the answer. Ignorance in others is also very revealing of a teacher's abilities and often demonstrates weaknesses in the pedagogical representation of concepts.

The teacher is not the culprit if the student doesn't want to learn.

It of course isn't intrinsically the fault of the teacher if the student enters the lecture theatre without any desire of paying attention or learn. Modern academic institutions are however subject to increasing financial pressures and must maintain a competitive edge both in their academic standing, that of their facilities, and all the stuff that contributes to that all-important world ranking. So that student with the intent of not engaging isn't an easy expulsion (financial reasons) and the pass standard of exams cannot be lowered... quality and flexibility of teaching is the most flexible constraint. And naturally, the quality of teaching isn't a universal standard, lecturing to a large audience is not an easy thing to do, and it's no surprise that's there are only a handful of truly great ones and that many people have remarked that they have found some concepts much easier to understand after seeing it presented slightly differently. It is also obviously a relatively personal taste of what levels of details a particular student needs to grasp a topic, but there are some truly awful lecturers out there.

[...] And if you want to ascribe any physical significance to the complex numbers, just look around you. The ubiquitous and affordable distribution of energy wouldn't be possible without the help of its application to engineering.

Really? How do complex numbers make energy affordable? Given that a lot of the challenges in the development of modern distribution systems have been from the lack of consideration beyond a first harmonic approximation, I'd have assumed the simplistic complex phasor representation has increased cost. Joking aside, modern systems are increasingly more non-linear, especially in RF and power conversion, phasors and a single imaginary number just don't give a clear picture. Take the original topic of this forum, for instance: there's be no direct analytical solutions proposed; a transmission line solution that omits the important initial propagation delay; or a computationally intense FDTD solution; (it is also possible to do some circuit rearrangements on a lumped x-line to get the propagation delay but in simple imaginary quantities the equivalent components become an ungodly order of polynomial). Just maybe there's a different/better/more-general transform to be found, or maybe it already has, but maybe listening to why some people don't even get along with Steinmetzian phasors may just help teachers and academics pick up the slack.

But If you want to go down the rabbit hole of the meaning of numbers, whatever numbers, just start asking what is so two about two that makes it a two and not a three, or a four? That has nothing to do with engineering itself. And if you don't know how to answer those questions, you cannot possibly advocate for the eradication of the use of the number two from engineering.

So, hypothetically, just as an example, I could advocate for their eradication if I did know why two wasn't three? Yeah, the philosophy of numbers, before saying it has nothing to do with engineering... perhaps have a little think first, just in case there's one little application area you've not considered.

[bsfeechannel]

How do complex numbers make energy affordable?

Have fun.

[penfold]

How do complex numbers make energy affordable?

[...]
Have fun.

"Do" is the present tense, the content of those videos is more about the early days, and the nature of electrical supply and consumption has changed somewhat since then. Anything to suggest that it is still the optimum solution?