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

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penfold:

--- Quote from: HuronKing on April 11, 2022, 08:03:10 am ---[...]

--- Quote ---You are so unable and unwilling to decouple the concepts of sqrt(-1), i, and then j (in engineering), that you are unable to understand my question.
--- End quote ---

Your question, or rather, the answer you want is fundamentally nonsensical. In asking, "does this icky part of mathematics I don't like actually exist?" you're rather asking "does mathematics exist?" Am I incorrect? If so, rephrase your question, please because you haven't actually formulated a question to be answered for pages and pages now.  >:(
[...]

--- End quote ---

See the previous reply for the slight segue. But without the formality of actual maths in engineering maths, the only thing we can do is have faith that somebody else has worked it out (again, not something I'm implicitly disagreeing with, it has to happen) but some people wonder and think about things beyond their remit which engineering teaching doesn't naturally answer and its a whole field of study on its own.

I just maintain with the ickiness of sqrt(-1), we often neglect the fact that it is less about being the square root of negative-one, which is a bit absurd in a natural context, but its value is in that it forms an orthogonal basis vector pair with positive-one, and a nicely closed algebraic system (you can add, multiply, divide, subtract entire vectors). In contrast, the i,j,k vector notation we typically use in vector calculus, is, however, a much more artificial construct where i,j,k are simply defined as orthogonal basis vectors with certain properties, but it is not a nicely formed algebraic system, multiplications, divisions, etc all need "special" treatment - not surprisingly, because an alternative was deemed icky circa 1900. But the alternative (geometric algebra) handles all those other aspects of physics so very nicely and permits interesting views of non-linearities... surely you can understand why somebody might want to question the relevance of sqrt(-1) when it stands so separately with the other ways in which we treat vector quantities in engiineering.

HuronKing:

--- Quote from: penfold on April 11, 2022, 09:22:45 am ---surely you can understand why somebody might want to question the relevance of sqrt(-1) when it stands so separately with the other ways in which we treat vector quantities in engiineering.

--- End quote ---

I can understand the question. It is why I found it interesting enough to spend pages and pages, and at this point, approaching weeks answering it. And it's a question I get every semester from students who I refresh on complex quantities before tackling basic power concepts (like power factor correction) and then transitioning that to more advanced ideas (like RF impedance matching). Showing these things on a whiteboard and having a lab full of equipment to test the applications is the best way to make them forget about Descartes.

What I start to lose patience with (not referencing to you) is when the conversation seems incapable of moving beyond the 17th century and their objections to complex numbers.  :-//

adx:

--- Quote from: hamster_nz on April 11, 2022, 12:26:47 am ---
--- Quote from: penfold on April 10, 2022, 09:47:12 pm ---My actual stance on the argument was that the teaching of maths and physics to engineers is often done without regard to the philosophy behind it.

--- End quote ---

I am actually quite glad this is true. The power of maths in engineering is it's utility - it's ability to solve actual problems, and give reliable meaningful answers. To question it too closely is a folly (and maybe even leads to madness).

We stand on the shoulders of giants, and pay researchers and academics to check their solidness and that of the foundations underneath them. Occasionally they do find interesting stuff... but a random person on the internet rejecting the legitimacy of sqrt(-1) on philosophical grounds after 450 years intensive research and demonstrated utility across many disparate fields is not noteworthy at all.

It is them cutting off their nose to spite their face.

--- End quote ---

I don't see the wrong with any of this except maybe that last line (even that has a ring of unavoidable truth to it).

I view maths as utilitarian (until this thread). Madness may be the necessary state of mind to appreciate some parts of it. We take a lot for granted, in that sense we might not know what we don't know, and might form many ideas that either over or underestimate the complexity of something. We trust, we make mistakes, we misapply. We occasionally question things. Some random person on the internet rejecting the legitimacy of sqrt(-1) on philosophical grounds after 450 years intensive research and demonstrated utility across many disparate fields ought not to be noteworthy at all. Yet all hell breaks loose.

penfold:

--- Quote from: HuronKing on April 11, 2022, 10:20:11 am ---[...] on a whiteboard and having a lab full of equipment to test the applications is the best way to make them forget about Descartes.

What I start to lose patience with (not referencing to you) is when the conversation seems incapable of moving beyond the 17th century and their objections to complex numbers.  :-//


--- End quote ---

Okay, you've hit the nail on the head. It is the unfortunately squishy aspect of the conversation but the one where my gripe is and kinda where engineering maths goes a bit against the grain, we prove things mostly through their utility (proof by utility... I like that phrase, dunno if it is any more widely applicable), I mean, I literally couldn't care less if any model used in engineering was or wasn't physically factual, so long as it gets the job done, its engineering, we are here to create. But, I do think that natural suspicion is a very reasonable thing to have, because, by intrinsically imbueing significance to the imaginary numbers, it conflicts with both the modern mathematical definitions (no numbers are natural) and the 17th century (some numbers are natural) views. But I can live with a third "engineering maths" definition of "anything goes".

TBH, its the same gripe I have with Poynting, it is a mathematical theorem of Maxwell's equations that we cannot contemplate avoiding, but it doesn't necesarily agree wiyh everything else when considered as a physical process... but the reason I let it slide is that it is a million times easier to explain than what might actually be going on... we'd first have to descover that, but I sruggle slightly in philosophically accepting it at DC along-side deBroglie (suggesting a wave with zero frequency carries zero momentum). Its just an internal pondering no rejection of the theories.

adx:

--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---
--- Quote from: adx on April 08, 2022, 11:53:44 am ---My view on those videos is it seems a bit fangrrlish and "story" rather than dry sequence of facts - which is totally appropriate for a YT video, but quoting it as evidence is similar to someone quoting a movie as evidence because it was well received and based on real events.

"how important Steinmetz work is" <> "complex numbers ... The ubiquitous and affordable distribution of energy wouldn't be possible without the help of its application to engineering."

Sounds utterly ridiculous to me,

--- End quote ---

It sounds ridiculous because you can't understand the implications of it. And you don't want to.

--- End quote ---

I can't understand what these implications I can't understand might be, and why I shouldn't want to. Me knowing so very little about everything, seems to be highly correlated with me having just told the truth.


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---
--- Quote ---His total work is much more than complex notation,
--- End quote ---

That's why I said that the "notation" helped. You need to improve your text interpretation skills.

--- End quote ---

"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."
and
"The content of those videos is about how important Steinmetz work is, exactly because it's still relevant to this very day."
You via those videos raised his entire work (or else was some veiled appeal to authority). "Help" relates not to whether all his work was used, but whether his complex numbers paper made possible the ubiquitous and affordable distribution of energy, or merely "helped" make it possible (as part of a greater team effort, I suppose that means). So no I got it right.

Except I now see I misread "its application to engineering" meaning physical significance of complex numbers rather than his complex numbers paper you were talking about just prior. That falsely made it seem even more ridiculous.


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---
--- Quote ---this seems to have been motivated more as a non-mathematical hack (optimisation),
--- End quote ---

What you talking about? Everything is a hack. We are hacking our way through existence since we discovered that chipped stone could be used for cutting tools and weapons.

Did Steinmetz discover a hack to ease the design and analysis of AC circuits? Praised be him. Hacking is what makes us humans, in the first place.

--- End quote ---

If that is really true, and I think it is, then we have nothing to argue about.

Except that hardly sets the best pedagogical direction when some hopeless miscreant, bowl in hand, looks up with pitiful eyes and says 'scuse me sir, can I borrow a penny, and oh what is the cosmic meaning of sqrt(-1)?

That's what caused the whole waffley texts incident.


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---
--- Quote ---and both he and Clarke seem not to have given two hoots (for the most part) about the mathematical basis of complex numbers and solutions when using this notation.
--- End quote ---

Why should they?

--- End quote ---

Because this contains the proof of sqrt(-1) I was sent to seek, and didn't find amongst the sensible content. I was expecting to see Descartes and Gauss battling it out through a numerically stable wormhole, saying things like "I welt thee with thine uninvertible matrices" to my wide-eyed astonishment.


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---... Some mathematician out there must have done that. And that's the beauty of applying math to engineering. You can use it with confidence because it is already proven to be logically sound. That's what math essentially is: language devoid of contradictions.

--- End quote ---

Ok, not really arguing with that. But if that's true, how do you tell which root of x^2+1 = 0 gets the +j? If you choose the wrong one, that's a contradiction.


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---
--- Quote ---Rather like HP's VNA - sqrt(-1) need not exist, because it is optional (I would like to suggest irrelevant) to the meaning of j.
--- End quote ---

Your argument about VNAs not representing (-1)½, or whatever, completely misses the point.

The Smith chart was invented taking into consideration complex numbers. So, if you want to properly understand the meaning of what you're reading on a Smith chart, you need to get into the mind of Phillip Smith, the engineer who invented it. And for that, you'll need to study complex numbers.

You're an engineer, not an hobbyist.

--- End quote ---

It's my entire point! Complex numbers as an engineering concept exist almost entirely separate from the sqrt(-1) definition.

But I see your point, Smith charts are built out of complex notation and its operators, and just looking at one (which is what most people perusing a datasheet do) is not "properly understand the meaning".


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---It's as simple as that. This has nothing to do with some kind of dogma, tradition, or whatever, as you like to insinuate.

--- End quote ---

It's all dogma and tradition if we don't question it.


--- Quote from: bsfeechannel on April 09, 2022, 05:01:24 pm ---
--- Quote ---And the unavoidable inference that it includes petroleum, solar etc.
--- End quote ---

O yeah, I hook up the fuel hose of my gasoline-powered blender to an outlet on the wall of my kitchen and make a delicious milkshake every morning.

--- End quote ---

That was just because of the hyperbolic nature of your cloud-scrapingly long-stalk flowery claim.

And I'm outta time tonight. I was trying to get caught up to the current page (assuming this doesn't push it over).

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