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"Veritasium" (YT) - "The Big Misconception About Electricity" ?
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adx:
I'm sure that sentiment is stretching the bounds of believability for many people here too. Sounds like you've been sniffing the chalk too long.

I can define a number 'line' based on 1 MOD 1 called moo numbers, and poke fun at anyone who suggests that 1 is not a moo number.

Yes no surprise I'd see something 'wrong' with 1's part as a complex number after "pretty much" and "peace sign", SiliconWizard's observation is closer to the mark though. And here I was thinking someone might pick up on the apparent contradiction of me talking about infinitesimal angle then saying rotation is an unavoidable consequence of i*i = -1.

Complex numbers can exist as a mathland fiction all they want, as a fundamental 'quantity' of nature if you like (I'm just not 100% convinced - it feels like a broken reality the way it has been put), but fundamental to electrical engineering? Real-valued measures of sines and cosines are not sqrt(-1), that idea is so ridiculous I shouldn't have continued arguing about it amidst the conflation with mathland fictions and quantum mechanical possibilities. That FFT I was talking about, like I said not a complex number in sight. Phasors, same.

I trolled myself.
bsfeechannel:

--- Quote from: adx on April 16, 2022, 02:38:41 pm ---I'm sure that sentiment is stretching the bounds of believability for many people here too. Sounds like you've been sniffing the chalk too long.
--- End quote ---

You get math all wrong. Math is not based on faith. Math is essentially a bunch of conveniently chosen postulates and another buch of theorems, which are deductions from those postulates, deductions which are based on another set of postules themselves.

What is a postulate? Essentially a provisory truth. Let me give you a crude example.

1. All Australians eat kangaroo meat.
2. Adx is Australian.
3. Therefore, adx eats kangaroo meat.

In the deduction above, I'm not asking you to believe in the first or the second postulates. I'm asking you to accept them as a provisory truths, i.e., if those are true, the conclusion (3) will be true.

But what happens if I eventually find out that adx is IRL a vegetarian? Well, that doesn't invalidate my reasoning, but certainly my choice of postulates doesn't help me model, describe or predict reality, does it?

So, the postulates upon which math theories are constructed have allowed these theories to have a wide range of applications and have stood the test of time. Should they be revised tomorrow because we find out that they are incomplete or that they do not cut the mustard anymore, they'll be abandoned, or updated.


--- Quote ---Complex numbers can exist as a mathland fiction all they want, as a fundamental 'quantity' of nature if you like (I'm just not 100% convinced - it feels like a broken reality the way it has been put), but fundamental to electrical engineering?
--- End quote ---

Fundamental in the sense that you'll have to deal with them one way or another.


--- Quote ---Real-valued measures of sines and cosines are not sqrt(-1), that idea is so ridiculous I shouldn't have continued arguing about it amidst the conflation with mathland fictions and quantum mechanical possibilities.
--- End quote ---

You shouldn't have skipped the classes on complex numbers.

$$\cos{x}=\frac{e^{ix}+e^{-ix}}{2}$$
$$\sin{x}=\frac{e^{ix}-e^{-ix}}{2i}$$
adx:

--- Quote from: bsfeechannel on April 18, 2022, 12:56:55 am ---
--- Quote from: adx on April 16, 2022, 02:38:41 pm ---I'm sure that sentiment is stretching the bounds of believability for many people here too. Sounds like you've been sniffing the chalk too long.
--- End quote ---

You get math all wrong. Math is not based on faith. Math is essentially a bunch of conveniently chosen postulates and another buch of theorems, which are deductions from those postulates, deductions which are based on another set of postules themselves.

--- End quote ---

I don't think the math itself is a system of belief, just what is "believed" about it.

At high school and for engineering it is approached as if it is something that must be accepted, shoulders of giants etc. If someone is unwilling or incapable of really getting into the nitty gritty of the proofs and philosophy, or simply doesn't have the time to satisfy all questions they might ever dream of, then they are taking it on faith. Being expected to trust in intellectual authorities with absolutely nil room for deviation is pretty much the definition of faith. All this talk of theorems, deductions and postulates is the setting up of a system to engender belief.

I'm not saying it is irrational, unreasonable or wrong. Just that in practical application it is faith.


--- Quote from: bsfeechannel on April 18, 2022, 12:56:55 am ---What is a postulate? Essentially a provisory truth. Let me give you a crude example.

1. All Australians eat kangaroo meat.
2. Adx is Australian.
3. Therefore, adx eats kangaroo meat.

In the deduction above, I'm not asking you to believe in the first or the second postulates. I'm asking you to accept them as a provisory truths, i.e., if those are true, the conclusion (3) will be true.

--- End quote ---

That may be true, but I don't quite get it - because it is a trick to get me (or perhaps you) to accept the postulates, your logic, and the conclusion. Where is my freedom to reject any of it? That could range from calling it all "rubbish" to simply saying I am not entirely convinced. Why is the latter so completely objectionable? What if my job relies on accepting it?

Or in the real case:
1 I don't eat kangaroo meat (that I remember).
2 I'm not Australian.
3 Therefore, I don't care (apart from the concept and ethics of eating zoo animals).

Why (in principle) should I accept a provisory truth if the reasoning that is brought to bear on them is irrelevant and the conclusion is uncertain?

What if I am the only Australian? A fact I discover after accepting the conclusion on the basis of what I thought was both sound and meaningful logic?

I choose not to believe in the process or the outcome. Not necessarily because of a philosophical objection, but because I don't enjoy it (while others seem to be having the time of their lives) - if you like call it spite. Science students are told to believe and they had better enjoy it. Applied mathematics seems there to be endured and never questioned from the outset.

Also my comment was about believably of the sentiment of you saying I think 1 is not a complex number. There is more to logic than logic, as I have alluded to above.

But if someone has a firm view that complex numbers are the fundamental 'quantity' which describes the world at large, then I'm sure it would seem like any deviation from that view is the wrong one.


--- Quote from: bsfeechannel on April 18, 2022, 12:56:55 am ---But what happens if I eventually find out that adx is IRL a vegetarian? Well, that doesn't invalidate my reasoning, but certainly my choice of postulates doesn't help me model, describe or predict reality, does it?

So, the postulates upon which math theories are constructed have allowed these theories to have a wide range of applications and have stood the test of time. Should they be revised tomorrow because we find out that they are incomplete or that they do not cut the mustard anymore, they'll be abandoned, or updated.

--- End quote ---

It kind of does invalidate the postulates and casts the reasoning into doubt. If it were taught that way, half the students would go away believing there is wiggle room. The alternative is to lead them into false belief in provisory truths. It's an unwinnable argument based on a sleight of hand.

I'm not against provisional belief, but unless you're a mathematics specialist, it is mostly acceptance and faith. Going against that causes friction, science suffers a similar problem but is somewhat manageable.


--- Quote from: bsfeechannel on April 18, 2022, 12:56:55 am ---
--- Quote ---Complex numbers can exist as a mathland fiction all they want, as a fundamental 'quantity' of nature if you like (I'm just not 100% convinced - it feels like a broken reality the way it has been put), but fundamental to electrical engineering?
--- End quote ---

Fundamental in the sense that you'll have to deal with them one way or another.

--- End quote ---

Where? Because it is popular and convenient? That's not fundamental, it's a circular argument. When something is as optional as it seems to be, arguments in support are expected to collapse into various logical fallacies.

An idea I kept forgetting to suggest, is a 'cheat sheet' of example(s) to demonstrate the fundamental (necessary) applicability (whatever that is) of sqrt(-1) to engineering, then that could help multitude(s) of 'disbelievers'. I'm not suggesting you or anyone here do it, it's just an idea that might work better than pointing to nonexistent proofs for bringing more hapless victims into the fold.


--- Quote from: bsfeechannel on April 18, 2022, 12:56:55 am ---
--- Quote ---Real-valued measures of sines and cosines are not sqrt(-1), that idea is so ridiculous I shouldn't have continued arguing about it amidst the conflation with mathland fictions and quantum mechanical possibilities.
--- End quote ---

You shouldn't have skipped the classes on complex numbers.

$$\cos{x}=\frac{e^{ix}+e^{-ix}}{2}$$
$$\sin{x}=\frac{e^{ix}-e^{-ix}}{2i}$$

--- End quote ---

I didn't. I might have slept through them, perhaps forgot it all or blocked it out. Who knows. Actually there is a story I'll mostly spare you where I did accidentally (due to injury) miss all the lectures of one of the maths classes of one type (I think linear algebra - had I gone I might have a better idea). I am usually pretty good at panicked cramming, but in that case it worked neither well nor at all.

But sines are not sqrt(-1). They are real-valued. I and Q representation doesn't require any sort of 'imaginary'. Despite an idea of complex frequency domain representation being supposedly embedded, it's not necessary. I'll just have to stick to my "that idea is so ridiculous I shouldn't have continued arguing about it".

Is there anything fundamentally unknowable about the quadrature signal in engineering?
bsfeechannel:

--- Quote from: adx on April 21, 2022, 04:42:51 am ---Being expected to trust in intellectual authorities with absolutely nil room for deviation is pretty much the definition of faith. All this talk of theorems, deductions and postulates is the setting up of a system to engender belief.
--- End quote ---

There is plenty of room for "deviation". The thing is that no one has been able, as of this day, to come up with something better.


--- Quote ---Science students are told to believe and they had better enjoy it.
--- End quote ---

What scientists are doing right now is putting all the known theories to the limit, either to confirm or to disprove them. I don't think science is a place for faith to thrive.
 

--- Quote ---Applied mathematics seems there to be endured and never questioned from the outset.
--- End quote ---

1 + 1 = 2. You can question it, but, before that, you need to understand why it is held true that 1 + 1 = 2.


--- Quote ---When something is as optional as it seems to be, arguments in support are expected to collapse into various logical fallacies.
--- End quote ---

You've got a point here. Cockroaches survive without math. However they're not engineers.

...Or are they?


--- Quote ---But sines are not sqrt(-1). They are real-valued.
--- End quote ---

Alas, you slept through the class where they demonstrated that ALL real numbers are complex, too.
SiliconWizard:
As we already said, there is no fundamental difference between irrational numbers and complex numbers (when having a non-zero imaginary part.) Both are defined by equations. Neither can *directly* be defined, so if your sense of what is "physical" and what is not is tickled here, both should tickle equally.

adx, you seem to be convinced that "real numbers" are physically real, while "complex numbers" are just a tool from human's imagination. That itself is a belief. It looks like the more accurate would be to say that you're "more comfortable" with real numbers, not that they inherently make more sense.

sqrt(2) is one solution of x^2 = 2. i is one solution of x^2 = -1. Big deal.

And, you have a problem with complex numbers because they are actually "two quantities" rather than just a single one.
But then you're OK with manipulating both sin and cos values, which are two quantities linked together.

Ultimately, I'm not sure this has really anything to do with science or reality, but mostly just with perception.

And IMHO, the universe and its physical reality does not freaking care about our qualms regarding numbers. It probably doesn't care about numbers altogether. Your perception does, and it's fine. Just maybe do not assume that you hold a "physical truth" just because it appears so in your own perception.
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