Author Topic: "Veritasium" (YT) - "The Big Misconception About Electricity" ?  (Read 279332 times)

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Offline hamster_nz

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1800 on: April 11, 2022, 12:26:47 am »
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.

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.
Gaze not into the abyss, lest you become recognized as an abyss domain expert, and they expect you keep gazing into the damn thing.
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1801 on: April 11, 2022, 03:06:53 am »
I'll buy it, to a degree. Timfox said "Stupidity, however, is being proud of one's ignorance." a page back.

You go a step further. You are proud of your own stupidity.

And after espousing the great power of artificial stupidity (AS) as the key to unlocking further human potential in machine-automated form, why do you think that would worry me? As I said, I've got to try harder than many, but I think I am doing quite well these days.

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I tend to think stupidity is more being unaware of one's ignorance (actually I haven't thought that through properly, but it sounds good).

Stupidity, as I said in other threads, is a moral issue. We offered you insight, you outright rejected it. So it is not a cognitive problem. You're not mentally incapacitated. You made the conscious choice of remaining ignorant.

Again with the ?

And again, I don't have to believe shit that isn't real.
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1802 on: April 11, 2022, 04:46:11 am »
What else is required to justify the use of a given mathematical method on a physical problem?

Did I ever say it wasn't? I just found sqrt(-1) a bit icky, and seeming to be used on human axiomatic faith without any other basis. I have learnt that it does have some other basis from bsfeechannel (possibly something I learnt years ago but forgot due to its absence from working tools and the RF "j"), but ultimately confirmed my suspicion about the human axiomatic faith thing as the "proof" I sought. So far.

I am now less inclined to question sqrt(-1)'s relevance in engineering, not because I have learned it makes me a target for some to assume I am a nincompoop who doesn't understand their field of training (although the latter did come as some surprise - it shouldn't of course), but because I actually did learn something here. HuronKing even took it as a partial win, and that is more helpful than not. Still, I don't have to believe shit that isn't real.
 

Offline HuronKing

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1803 on: April 11, 2022, 08:03:10 am »
Still, I don't have to believe shit that isn't real.

I thought about writing a detailed reply to the your last post.

But this latest one shows that at the end of all this - you still don't understand complex numbers. You still think there is some ascribed meaning to the terms 'real' and 'imaginary.'  :palm:

THERE... IS... NOT!!! It's not. Those names are the fairy tale fiction - not the concepts they are ascribed to. For the last time: get your mind out of the 17th century.  |O

You keep accusing me, and others, of having axiomatic faith and 'convictions' and whining about belief systems with comments like this,
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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.

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.  >:(

In any case, the complex numbers ARE our system of numbers. If positives, negatives, exponentials, sines, cosines, logarithms, fractions, addition, subtraction, multiplication, etc etc etc can all have "innate physical meaning" then so too do the complex 'icky' imaginary numbers. They are all tied together. There is no escaping that fact - if you don't (want to) believe it, you don't believe math.

Or, NOTHING in mathematics has "physical meaning." And I'm actually fine with taking that position - I've never seen the number "3" so who is to say that the concept of "3" exists in anything other than our minds? That has nothing to do with sqrt(-1) though. That is just how to be logically consistent. Either you accept mathematics as it's been proven or you don't. In either case, the same axioms that give us all the other numbers lead us, inexorably, to the complex numbers. That's what centuries of mathematical investigation has led us to.

The proofs are involved but they aren't impossible. You have constructed a peculiar insulation against the proofs though. That is, anything simple or introductory is too trivial but anything rigorous is "appeal to authority" and too hard and you'd rather just not believe it...

However, mathematics has this peculiar quality that its rules of logic seem to be applicable to the physical world. The conclusions we have drawn about complex numbers are remarkably useful and have many physical applications whose cases have been proven ad nauseam at this point.

This is, in fact, the opposite of a religious conviction. I'm not hanging my hat on made-up terminology by a 17th century mathematician about what constitutes 'real' things (your continued insistence on doing so is the actual definition of appeal to authority here). I have to use Descartes' terminology for historical reasons - nothing more. Rather, I have learned what these numbers mean - both in the conceptual mathland world and our physical world. I've utilized them to solve actual problems. You've apparently never done so. That's cool.

 

Offline penfold

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1804 on: April 11, 2022, 08:59:54 am »
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.

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.

Yeah, I'm not disagreeing with you, it would be utterly absurd to actually teach it and to start questioning (in anything other than a "what if") whether it's actually correct. I'm pretty sure we know that our discussion here doesn't carry any particular weight so it's not as if we're nailing a petition to the gates of the IEEE. However, without the teaching of a specific philosophy from which the numbers are produced and attributed meaning in the world, though they are taught with a highly comprehensive user manual if the user is forced to attribute or question their origin from only their natural human instincts, then there's a bit of a problem because modern mathematics has a much more "defined" and abstract definition than historically... again, it's not a problem with the maths or physics itself, but with the person's interpretation, if and only if they think about it to question it.

So, when we discuss the utility or real-ness of complex numbers, it isn't to say that they don't exist, or are wrong, or don't exist on paper, but whether any better "understanding" could be produced by a slightly different teaching method perhaps. Regardless of whether or not one can read a textbook, accept the details as (in a philosophical sense) absolute fact, there can still be a bit of a miss-meshed gear in the back of your mind that doesn't totally accept it. I'm just hypothesising that perhaps maybe a slightly more rigorous treaching method could be of benefit.

But equally, the converse of that is true when it comes to engineer's understanding the underlying physics, we are expected to do so, but with that we (as engineers) must accept certain mathematical consequences as if they were the underlying mechanism, except we must do that in the kind of environment where several different physics viewpoints meet. We could easily have an LED (a largely quantum process) in series with a resistor (a circuit theory construct) flashed at a high rate (hello, Poynting), but it is also non-linear and not purely sinusoidal... so again, I reiterate... it is not an especially difficult thing to solve, but it breaks that natural intuition and the conventional methods would be highly approximate.

The trouble is, it is an immensely difficult conversation to have in typed words and you kinda have to commit to a viewpoint when deciding to reply, which often involves assuming a lot more information than is actually provided in each post... its fun though.
 

Offline penfold

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1805 on: April 11, 2022, 09:22:45 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.

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.  >:(
[...]

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.
 

Offline HuronKing

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1806 on: April 11, 2022, 10:20:11 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.

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.  :-//
« Last Edit: April 11, 2022, 10:22:22 am by HuronKing »
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1807 on: April 11, 2022, 11:43:33 am »
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.

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.

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.
 

Offline penfold

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1808 on: April 11, 2022, 01:49:21 pm »
[...] 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.  :-//


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.
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1809 on: April 11, 2022, 03:35:31 pm »
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,

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

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.

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His total work is much more than complex notation,

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

"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.

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this seems to have been motivated more as a non-mathematical hack (optimisation),

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.

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.

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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.

Why should they?

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.

... 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.

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.

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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.

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.

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".

It's as simple as that. This has nothing to do with some kind of dogma, tradition, or whatever, as you like to insinuate.

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

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And the unavoidable inference that it includes petroleum, solar etc.

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.

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).
 

Offline HuronKing

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1810 on: April 11, 2022, 04:47:37 pm »
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".

Please show me where modern mathematical definitions say "no numbers are natural." I don't understand what this means. ???

Mathematicians of the 17th century barely understood calculus. Descartes, to his credit, laid the foundation with analytic geometry but he didn't know how to take a derivative. He was close, but he still wouldn't be able to pass a 1st semester calculus course with the extent of his knowledge. In a very big sense, you and I are WAY smarter than Descartes. You and I can solve differential equations and integrals Descartes could never even imagine.  8)

Nature is more complex than just what we can count on our fingers and toes and it often violates our intuition. Yet, for some reason, nature seems to obey logical mathematical rules.

As another example, what is 0 times infinity? 0 divided by 0? Infinity divided by 0?
https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

Answers to these questions are impossibilities for (pre-calculus) 17th century mathematics - yet they do have answers... under the right conditions and their answers directly correlates to physical meaning:
https://lhospitalsrule.weebly.com/real-world-applications.html

There is a huge amount of things in mathematics that ought to philosophically bother you, not just the complex numbers, if you must restrict yourself to only what you can count on your fingers and toes. And maybe the idea of solving an equation which asks "what's infinity divided by 0" does bother you too.   ;D

Neither mathematics nor engineering compels us to restrict ourselves to what is perceptible to our intuition. Our intuition is often wrong. And we have lasting evidence of what relying on faulty intuition gets us (bad terminology for mathematical definitions for starters  ;) ).  Follow the logic, bravely, and see where it takes you (hopefully not back to 1657).

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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.

Because we have to operate within the paradigms of the theory. You have to be careful when trying to extend classical electromagnetism (Heaviside didn't know about photons) to quantum physics.
 

Online TimFox

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1811 on: April 11, 2022, 04:58:24 pm »
I was taught that the "natural numbers" are the positive integers (not including zero).  An older name is "counting numbers".
Some mathematicians include 0 in the set of natural numbers, but others prefer "whole numbers" or "non-negative integers" for the set including 0.
Historically, the number zero is a later concept than the other integers.
By the way, the "rational numbers" are not ones that are less icky or more sane than "irrational numbers", they are numbers that can be expressed as a "ratio" of two integers.
When communicating with other technical people, it is salutary to use standard names for well-understood concepts.
« Last Edit: April 11, 2022, 05:05:14 pm by TimFox »
 
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Offline SiliconWizard

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1812 on: April 11, 2022, 05:44:13 pm »
I was taught that the "natural numbers" are the positive integers (not including zero).  An older name is "counting numbers".
Some mathematicians include 0 in the set of natural numbers, but others prefer "whole numbers" or "non-negative integers" for the set including 0.

I have myself learned that the set N of natural numbers included zero, and the notation to exclude zero from it was writing N*. (Same for Z and Z*...)
(Btw, do you consider zero to be part of Z?)
But it seems to differ depending on where you have learned. From a lot of material I read over the years, I'm under the impression that N excluding zero is a common notation in the USA, while using N and N* seems more common in Europe. Just personal observation here.

As to irrational numbers, they are in essence *roots* of some equations, that can't be expressed as rational numbers. So we can only express them implicitly via some equation.
sqrt(2) as usually defined is the principal root in R of the equation x^2 = 2. Likewise, i is the principal root in C of the equation x^2 = -1. In both cases, they are defined are roots of some equation.
Whether you consider them something "real" or just a "handy trick" is more philosophical than technical.


 

Online TimFox

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1813 on: April 11, 2022, 06:19:08 pm »
Yes.  The word "irrational" just means that the root in question cannot be expressed as the ratio of two integers.  (Pi is not 22/7.)
 

Offline penfold

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1814 on: April 11, 2022, 11:09:19 pm »
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".

Please show me where modern mathematical definitions say "no numbers are natural." I don't understand what this means. ???
[...]

My apologies, I wasn't paying attention, I didn't mean natural mathematically, I meant natural, philosophically, in the sense of being of or directly or closely related to natural things, say, quantities of countable things or something perceivable to humans: a number of sticks in a pot would represent the same quantity to two people regardless of the language or abstraction thereof. Rational numbers in the same way, as they can be formed (often, for most quantities) from fractions of units. Irrational numbers... that's a whole other discussion.

I can't recall immediately a good reference and I'm away from home for the week so it'll be a little while before I can dig for the right citation. Any generic set theory and mathematical logic textbook should give an idea how the more axomatic and less physical significance of "numbers" overtakes in a more modern sense. Think about how you might word it if you were to describe the equation or process using words, i.e. are you directly multiplying a length or are you multiplying numbers that represent the number of unit lengths, then what is the result and how would you then represent that physically, is there a measurement process used in between and how do you get from the written number to the physical quantity... its unfortunately one of those things that takes a lot of reading of lots of different books and single explanatory references aren't very common.

But, your reference to l'Hopital sums it up so nicely, as you lead into it with "As another example, what is 0 times infinity? 0 divided by 0? Infinity divided by 0?", suggests you havn't quite understood the question yourself, l'Hoptital it would give the value to a function that contains terms that individually tend to those values... not of the pure numbers themselves necesarily.
The complexities of nature are kinda irrelevent to the maths, the maths describes only our observations and patterns amongst them, it all exists within the artificial construct of logic that is related to human reasoning, nature just does its own thing.

[...]
Because we have to operate within the paradigms of the theory. You have to be careful when trying to extend classical electromagnetism (Heaviside didn't know about photons) to quantum physics.

Yeah... exactly... they both agree mathematically, but rely on very different implications towards physical processes, so it becomes a question of observeable quantities - so at the same time as apprechiating the limits of the theories one must also be careful of what the maths implies about physical processes - so when we are so quick to say that Poynting explains something, (rhetorical question) are we simultaneously saying that it is the genuine underlying physical process? I suspect you still havn't worked out that my gripe is not with maths itself, but with how people are so quick to ignore the fact it is only describing links between the observations etc, and whilst can (and has) predict(ed) other physical phenomena, the purely mathematical proof does not itself proove something physically.
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1815 on: April 12, 2022, 04:55:40 pm »
Still, I don't have to believe shit that isn't real.

I thought about writing a detailed reply to the your last post.

But this latest one shows that at the end of all this - you still don't understand complex numbers. You still think there is some ascribed meaning to the terms 'real' and 'imaginary.'  :palm:

THERE... IS... NOT!!! It's not. Those names are the fairy tale fiction - not the concepts they are ascribed to. For the last time: get your mind out of the 17th century.  |O

Ok, hopefully I can explain this part a bit better.

True - I still don't understand complex numbers.

I hope I'm not letting the terms 'real' and 'imaginary' directly drive my thoughts, as you rightly point out this would be trust in mere words.

But they do have an unavoidable historical ascribed meaning which for hundreds of years was accepted to be "true" by some of the greatest minds etc - the very basis on which it is now argued that the new meaning is justified. What's to say it won't shift again?

Also a while back you said "... We call them photons, because calling them corpuscles would carry with it a lot of baggage from Newton's other arcane ideas." - this works both ways, implying that real and imaginary remain current terms because the old meaning finds some support to this day, despite objections from some quarters. (It could be because the concept never went away, while the "corpuscle" theory did for a while.)

If they were called "lateral" maybe I would be less inclined to ask "how so?", but that's only because I'd assume defined meaning from the name. It's the same objection and ultimately solves nothing.

People who disagree with sqrt(-1) are disagreeing with a concept for the same reasons the name got invented - and that has meaning.

You keep accusing me, and others, of having axiomatic faith and 'convictions' and whining about belief systems with comments like this,
...

Unfortunately in trying to understand your questions here, I get more of a sense of belief and inability to see what I mean.

I'm not suggesting it is wrong. If you're right you're right and you won't want to change that. It'd be like having to accept a deluded person's delusions before moving forward.

I don't think I can rephrase my question any better in a practical sense, penfold has put things better than possibly I ever could.

No I am not asking "does mathematics exist?".

Correct - I don't believe math (not entirely / implicitly). "Never trust the math." I said. That is for philosophical reasons (it's not the shit that I find to be unreal). Strangely I think I have seen the number 3 (I thought about this when you said it before), it could be that that is what drives my particular and peculiar (or not so) disbelief (skepticism). I'm not denying the concept of imaginary numbers, they can exist in mathland all they want.

I can't even imagine what a proof would look like. I'd like to see one. (This would not be on how they are used, but why innate physical meaning, and to shed light on what they are.)

All my objections to imaginary numbers in engineering disappear for polar notation (for obvious reason). I just prefer complex notation and operations.

Mathematics is (or is supposed to be) a rational belief system. With that comes baggage. Not believing it (different from rejecting its existence) helps me with that.

I don't understand why you would persist in saying I've apparently never used complex numbers in (I guess) engineering, over an indistinct philosophical objection.
 

Offline hamster_nz

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1816 on: April 12, 2022, 11:15:26 pm »
Mathematics is (or is supposed to be) a rational belief system.

Um, I think there is your problem...  For the large part Mathematics isn't a "belief system (although it is has been mathematically proven to be a bit rotten at the core from around 1930 or so...).

Maybe you follow the thoughts of Eugene Wigner?

https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Gaze not into the abyss, lest you become recognized as an abyss domain expert, and they expect you keep gazing into the damn thing.
 

Offline bsfeechannel

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1817 on: April 13, 2022, 01:07:19 am »
It's my entire point! Complex numbers as an engineering concept exist almost entirely separate from the sqrt(-1) definition.

Nope. $$\sqrt{-1}$$ is how complex numbers first revealed themselves. It kept creeping up after people started to tinker with negative numbers.

Then someone decided to investigate it a little deeper. They literaly discovered a whole new dimension for numbers that could, as it happens with whatever number, be used to quantify all sorts of things, including those related to engineering.

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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".

If you look at a Smith chart you need to understand what those quantities mean. And they are all complex, composed of a real and an imaginary part, you know, that one that is multiplied by that pesky $$\sqrt{-1}$$ found centuries ago, with exactly the same meaning.
« Last Edit: April 13, 2022, 01:10:45 am by bsfeechannel »
 
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Offline HuronKing

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1818 on: April 13, 2022, 02:04:32 am »
My apologies, I wasn't paying attention, I didn't mean natural mathematically, I meant natural, philosophically, in the sense of being of or directly or closely related to natural things, say, quantities of countable things or something perceivable to humans: a number of sticks in a pot would represent the same quantity to two people regardless of the language or abstraction thereof. Rational numbers in the same way, as they can be formed (often, for most quantities) from fractions of units. Irrational numbers... that's a whole other discussion.

This is an incredibly peculiar thing to say given what you're suggesting about only 'natural numbers' (a squishy philosophical definition you're making up) being okay and not the complex numbers.

Why are irrationals a whole other discussion?

Pi, an irrational number, is just the ratio of a circle's circumference to it's diameter. There is, in fact, absolutely nothing unnatural about it. It is one of the most 'natural' numbers in existence! Both abstractly and physically.
Our only problem is we can't write all the digits of pi on a piece of paper. Is that really a problem though? But I guess pi, like sqrt(-1), is super mysterious and mystifying and has also been suddenly branded as icky in this conversation because we can't count it on our fingers... we're not even in the 17th century anymore. Welcome to ancient Babylon apparently...  ::)

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I can't recall immediately a good reference and I'm away from home for the week so it'll be a little while before I can dig for the right citation. Any generic set theory and mathematical logic textbook should give an idea how the more axomatic and less physical significance of "numbers" overtakes in a more modern sense. Think about how you might word it if you were to describe the equation or process using words, i.e. are you directly multiplying a length or are you multiplying numbers that represent the number of unit lengths, then what is the result and how would you then represent that physically, is there a measurement process used in between and how do you get from the written number to the physical quantity... its unfortunately one of those things that takes a lot of reading of lots of different books and single explanatory references aren't very common.

The more axiomatic and abstract our mathematical system has gotten, the more useful it has become. Thank goodness we don't just count on our fingers and toes anymore... the power of mathematics is that it is so well abstracted yet logically rigorous that it's application, and prediction of the solutions, for physical phenomena is one of the best things humanity has collectively devised.

You can go round and round chasing your tail about whether math is 'physical' unless you're counting sheep or whatever. I'm not worried about that. Math is logic and the universe is, evidently, logical. Complex numbers round out the whole of our algebraic number system and have a host of useful applications with as much evidentiary merit as irrational numbers, transcendental numbers, negative numbers, and even zero. Somehow this isn't enough evidence of the 'physicality' of complex numbers (lest I say you must throw out all the other math that gets taken for granted).

But sure, some people would rather huddle around and dismiss it all as philosophical mumbo jumbo ickiness because they can't find sqrt(-1) between their thumb and forefinger.

At this point... whatever.

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But, your reference to l'Hopital sums it up so nicely, as you lead into it with "As another example, what is 0 times infinity? 0 divided by 0? Infinity divided by 0?", suggests you havn't quite understood the question yourself, l'Hoptital it would give the value to a function that contains terms that individually tend to those values... not of the pure numbers themselves necesarily.

You haven't understood the example. I'm not motivated enough to explain it further given what else I'm reading here.

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The complexities of nature are kinda irrelevent to the maths, the maths describes only our observations and patterns amongst them, it all exists within the artificial construct of logic that is related to human reasoning, nature just does its own thing.

Yet there are some here who want to reduce both nature, and our math, to nothing more compelling than counting on fingers and toes.

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Yeah... exactly... they both agree mathematically, but rely on very different implications towards physical processes, so it becomes a question of observeable quantities - so at the same time as apprechiating the limits of the theories one must also be careful of what the maths implies about physical processes - so when we are so quick to say that Poynting explains something, (rhetorical question) are we simultaneously saying that it is the genuine underlying physical process? I suspect you still havn't worked out that my gripe is not with maths itself, but with how people are so quick to ignore the fact it is only describing links between the observations etc, and whilst can (and has) predict(ed) other physical phenomena, the purely mathematical proof does not itself proove something physically.

I suspect you still haven't worked out my position if you think I've suggested that. I'm growing tired with this whole thread. I'm only writing one more response to adx and then I'm done. You and adx can have the last word.
 

Offline HuronKing

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1819 on: April 13, 2022, 02:30:36 am »

I hope I'm not letting the terms 'real' and 'imaginary' directly drive my thoughts, as you rightly point out this would be trust in mere words.

But they do have an unavoidable historical ascribed meaning which for hundreds of years was accepted to be "true" by some of the greatest minds etc - the very basis on which it is now argued that the new meaning is justified. What's to say it won't shift again?

You say you're not letting it drive your thoughts... RIGHT BEFORE YOU SAY THAT YOU ARE LETTING IT DRIVE YOUR THOUGHTS.

For someone who cried about appeals to authority - THIS IS THE ULTIMATE APPEAL TO AUTHORITY.

I've told you over, and over, and over again to get the ascribed meaning out of your head because it has no logical or evidentiary basis to support it - just Descartes' own ignorance. You won't do it.

If you're asking why it won't shift again - you evidently haven't been reading any of the links I've been posting. I grow weary with this. Here is one more link - Richard Feynman has a lecture about this. Read it, listen to it (the recordings are on the site), set it on fire for being too icky, whatever you want to do.
https://www.feynmanlectures.caltech.edu/I_22.html

And Feynman, great educator as he was, specifically addresses your objection:
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Now you say, “This can go on forever! We have defined powers of imaginaries and all the rest, and when we are all finished, somebody else will come along with another equation which cannot be solved, like x6+3x2=−2. Then we have to generalize all over again!” But it turns out that with this one more invention, just the square root of −1, every algebraic equation can be solved! This is a fantastic fact, which we must leave to the Mathematics Department to prove. The proofs are very beautiful and very interesting, but certainly not self-evident. In fact, the most obvious supposition is that we are going to have to invent again and again and again. But the greatest miracle of all is that we do not. This is the last invention. After this invention of complex numbers, we find that the rules still work with complex numbers, and we are finished inventing new things. We can find the complex power of any complex number, we can solve any equation that is written algebraically, in terms of a finite number of those symbols. We do not find any new numbers. The square root of i, for instance, has a definite result, it is not something new; and ii is something. We will discuss that now.
-- Feynman 22-5

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Also a while back you said "... We call them photons, because calling them corpuscles would carry with it a lot of baggage from Newton's other arcane ideas." - this works both ways, implying that real and imaginary remain current terms because the old meaning finds some support to this day, despite objections from some quarters. (It could be because the concept never went away, while the "corpuscle" theory did for a while.)

This is nonsensical reasoning. We went over it, pages ago, that Gauss himself remarked that Descartes' idiotic naming convention made sqrt(-1) sound spooky to a generation of mathematicians. It is impossible to overstate the influence of Descartes on mathematics (he has a whole coordinate system named after him).

So... yea... you're appealing to authority, man.

"Well lots of people kept calling it a weird spooky sounding thing so it must have a kernel of truth to it despite all the historical and mathematical evidence to the contrary."

Wow, amazing reasoning. Such smart. Very compelling. You win.

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If they were called "lateral" maybe I would be less inclined to ask "how so?", but that's only because I'd assume defined meaning from the name. It's the same objection and ultimately solves nothing.

So things only make sense to you if they're named right? That's it? I'm willing to concede the name is confusing at first... but that this is what we're now arguing about your reticence to accept it... fine... you win. Enjoy.

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People who disagree with sqrt(-1) are disagreeing with a concept for the same reasons the name got invented - and that has meaning.

Who disagrees with sqrt(-1)? Please - names from the 20th century only please... and high school students don't count.
This is rhetorical. I don't really care who 'disagrees with sqrt(-1)' because I can comfortably write them off as mathematically illiterate. There is a reason every high school algebra course teaches complex numbers and a reason every electrical engineering curriculum includes a refresher of complex numbers. Those reasons have nothing to do with the numbers being spooky and we just love telling ghost stories.

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Unfortunately in trying to understand your questions here, I get more of a sense of belief and inability to see what I mean.

You don't understand my simple questions? The trouble is, as I said, is I do know what you mean. The issue is you don't like my answers or the answers of any of the references I've posted. Whatever.

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I'm not suggesting it is wrong.

No I am not asking "does mathematics exist?".

Correct - I don't believe math (not entirely / implicitly). "Never trust the math." I said.

"Math isn't wrong... but I don't believe it."

Yea, you can see why I'm not going to waste my time with this garbage anymore.

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All my objections to imaginary numbers in engineering disappear for polar notation (for obvious reason). I just prefer complex notation and operations.

You object to the imaginary numbers... but you prefer complex notation...

Dude... you can't write complex notation without... you know what... no. I'm not continuing down this path of incoherent lunacy.

That's it. I'm done. You win.
« Last Edit: April 13, 2022, 02:40:52 am by HuronKing »
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1820 on: April 13, 2022, 07:32:35 am »
Mathematics is (or is supposed to be) a rational belief system.

Um, I think there is your problem...  For the large part Mathematics isn't a "belief system (although it is has been mathematically proven to be a bit rotten at the core from around 1930 or so...).

I (naturally) disagree. For the large part mathematics is a belief system. Are you saying you don't believe it?

A while back I said "we can't have negative length". You then said "And yes you can measure a negative length, you just need to be careful about defining your basis vectors." despite knowing no one would answer "how long is a piece of string" with "oh, -1m". What made you say that?

The entire purpose of educating students seems to ultimately get them to believe things they can go on to (never) use. Especially engineering math.

Maybe you follow the thoughts of Eugene Wigner?

Interesting, I hadn't seen that before. Yes that sort of thing, but more from the point of view of (naturally) some of the criticisms. It's just around the themes of people fooling themselves.
 

Offline penfold

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1821 on: April 13, 2022, 09:36:55 am »
I suspect you still haven't worked out my position if you think I've suggested that. I'm growing tired with this whole thread. I'm only writing one more response to adx and then I'm done. You and adx can have the last word.

Fair enough, anything I write still remains open to criticism from others.

[...] I meant natural, philosophically, in the sense of being of or directly or closely related to natural things, say, quantities of countable things or something perceivable to humans[...]
This is an incredibly peculiar thing to say given what you're suggesting about only 'natural numbers' (a squishy philosophical definition you're making up) being okay and not the complex numbers.

It's not a squishy definition that I've made up, it is quite an established concept... the concept of being a "natural entity" at least is, I just stretched the definition to numbers, there is a good treatment of that in Mill's Ratiocinative and Inductive Logic (much of the work isn't unique to Mill, but compiled into a cohesive system written natively in English avoids some of the poorer translations of others'). A reference I totally forgot about was this site of Peter Smith which does go quite some way to demonstrate how maths is simply a branch of philosophy and that philosophy isn't as squishy as you may think (i.e. not just about drinking wine and pondering).

Why are irrationals a whole other discussion? [...] we can't count it on our fingers... we're not even in the 17th century anymore. Welcome to ancient Babylon apparently...  ::)

Irrationals are a whole other discussion because there is not necessarily a perfect and infinitely precise process for representing them physically, the emphasis there on "process", whilst a rational number would be as difficult to represent to some arbitrary precision, an irrational would require an infinite precision no matter how precise the process was... which is a whole other discussion, because that is possible with some, maybe not all.
Again, you are missing my point, modern maths does away with the dependency on physical representation by abstracting it beyond that necessity of representing numbers physically. In the more modern maths and natural philosophy, the "on-paper" representation of maths does not necessitate that the numbers are physically representable (i.e. avoiding the problems of geometric proofs) - yet, what you are doing by teaching complex numbers as immediate physical concepts is incredibly 17th century, whereas what I am suggesting is that the complex numbers could just be taught for what they are as just one possible representation of a vector.

like sqrt(-1), is super mysterious and mystifying and has also been suddenly branded as icky in this conversation because we can't count it on our fingers

I think you are slightly biased from your teaching experiences, that is certainly not what I am suggesting. I am still suggesting that there is a difference between "maths as an abstract language" and the physical processes it describes. The power gained by modern maths through that abstraction is in the fact we can work with totally realisable numbers and separately bridge between the number on paper to the physical quantity through isomorphism and metrics... that is especially implicit in engineering, it is something we often do without thinking, i.e. the rms of a 1V pk sine-wave, maybe 1/sqrt(2) on paper, but could be 1.707 with some uncertainty as far as we can measure. The complex j is not immediately there on the scope, we just add that on when representing it on paper.

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The more axiomatic and abstract our mathematical system has gotten, the more useful it has become. Thank goodness we don't just count on our fingers and toes anymore...

So why insist on breaking that nice abstraction by teaching complex numbers as non-abstract things?

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You can go round and round chasing your tail about whether math is 'physical' unless you're counting sheep or whatever. I'm not worried about that. Math is logic and the universe is, evidently, logical.

Again, (modern) maths is not itself physical, I have no problem with that, only when somebody says it is. But... the universe isn't necessarily logical, science is logical and the behaviours and patterns arrived at through scientific study are logical, but only within science... that's the squishier end of philosophy, I mean, we don't know with complete certainty that the bible is wrong, only that is doesn't agree with the concepts arrived at through science.

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But sure, some people would rather huddle around and dismiss it all as philosophical mumbo jumbo ickiness because they can't find sqrt(-1) between their thumb and forefinger.

At this point... whatever.

I'm sorry you feel that way.

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But, your reference to l'Hopital sums it up so nicely, as you lead into it with "As another example, what is 0 times infinity? 0 divided by 0? Infinity divided by 0?", suggests you havn't quite understood the question yourself, l'Hoptital it would give the value to a function that contains terms that individually tend to those values... not of the pure numbers themselves necesarily.

You haven't understood the example. I'm not motivated enough to explain it further given what else I'm reading here.

How many other interpretations could there be? l'Hopital doesn't relate to the question as you wrote it.

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Quote
The complexities of nature are kinda irrelevent to the maths, the maths describes only our observations and patterns amongst them, it all exists within the artificial construct of logic that is related to human reasoning, nature just does its own thing.
Yet there are some here who want to reduce both nature, and our math, to nothing more compelling than counting on fingers and toes.

Exactly, but I'm hypothesizing that where a lot of the philosophy and relationship between mathematical and the physical world get mixed up into a "the maths works out, therefore it must be physical", so yes, to most of the world, without being taught the more formal logic and constructs behind maths, what else do they have to go on? Just the word of a teacher?

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[...] I suspect you still havn't worked out that my gripe is not with maths itself, but with how people are so quick to ignore the fact it is only describing links between the observations etc, [...]
I suspect you still haven't worked out my position if you think I've suggested that.[...]

I suspect you think I may be attacking you personally if you suspected that I suspected that of you, because I didn't and I'm not.
 

Offline snarkysparky

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1822 on: April 13, 2022, 12:08:30 pm »
If i asked you to plot for me a sin function on the whiteboard with frequency F  and magnitude M could you do it to my satisfaction  ??


You would try and I would say WRONG!!!

The sin function I want goes through zero when its argument value is pi.

So you see to do it my satisfaction you would need to know the phase of the sin function I had in mind.   I could be a piece of machinery that expects a sinusoidal input at a certain phase.

This is the imaginary part. 

 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1823 on: April 13, 2022, 12:26:24 pm »
WTF
 

Offline adx

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Re: "Veritasium" (YT) - "The Big Misconception About Electricity" ?
« Reply #1824 on: April 13, 2022, 03:03:39 pm »
Nope. $$\sqrt{-1}$$ <stuff>

O altar up on high, may I erect my feeble ladder up unto thee.

Nope and nope. I meant sqrt(-1) hardly factors (non-mathematical meaning) into complex phasors.

If you mean Steinmetz purloined the concept because it seemed to fit but most of all it worked, then all power to your argument, and may your feeble ladder become reinforced with the sweet fruits and vines and structurally graded tree stems of delight. But it sounds like you're saying angels sent down (or up, depending on your basis vectors) complex numbers before angles.

If I look at a Smith chart, for a start I don't really understand what those quantities mean because it's RF and who does, but I do see reactances and similar things. A complex composed of a real and a, you guessed it, nother real part (and a fake "+" sign). Word generation warning: I'll call it a vec-tor.

sqrt(-1) has "exactly the same meaning" as 90 degrees CCW? a physical axis? a frequency-dependent time delay? a polar notation phasor has sqrt(-1) at its heart? O altar o proof, where artst thou?

I don't hold Steinmetz responsible for high treason, he never suggested they are the same thing afaik. Maybe you're not.
 


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