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

--- Quote from: adx on April 05, 2022, 04:24:43 pm ---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.

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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:

--- Quote from: SiliconWizard on April 05, 2022, 05:50:11 pm ---
--- Quote from: adx on April 05, 2022, 04:24:43 pm ---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.

--- End quote ---

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.

--- End quote ---

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:

--- Quote from: TimFox on April 05, 2022, 05:33:07 pm ---18th and 19th century mathematics is something that happened to other people.

--- End quote ---

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:

--- Quote from: HuronKing on April 05, 2022, 04:52:43 am ---
--- Quote from: adx on April 05, 2022, 04:23:31 am ---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.
--- End quote ---

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.

--- End quote ---

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:


--- Quote from: HuronKing on April 05, 2022, 04:33:43 pm ---
--- Quote ---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."
--- End quote ---
— R. Penrose

--- End quote ---

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.


--- Quote from: HuronKing on April 05, 2022, 04:52:43 am ---
--- Quote ---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).
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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!!!!  >:D

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

--- End quote ---

That is the look I am going for.


--- Quote from: HuronKing on April 05, 2022, 04:52:43 am ---
--- Quote ---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.
--- End quote ---

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

--- End quote ---

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.
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