General > General Technical Chat
"Veritasium" (YT) - "The Big Misconception About Electricity" ?
hamster_nz:
--- 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.
adx:
--- Quote from: bsfeechannel on April 10, 2022, 06:57:55 pm ---
--- Quote from: adx on April 10, 2022, 02:04:51 pm ---I'll buy it, to a degree. Timfox said "Stupidity, however, is being proud of one's ignorance." a page back.
--- End quote ---
You go a step further. You are proud of your own stupidity.
--- End quote ---
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.
--- Quote from: bsfeechannel on April 10, 2022, 06:57:55 pm ---
--- Quote ---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).
--- End quote ---
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.
--- End quote ---
Again with the ?
And again, I don't have to believe shit that isn't real.
adx:
--- Quote from: TimFox on April 09, 2022, 03:56:09 pm ---What else is required to justify the use of a given mathematical method on a physical problem?
--- End quote ---
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.
HuronKing:
--- Quote from: adx on April 11, 2022, 04:46:11 am ---Still, I don't have to believe shit that isn't real.
--- End quote ---
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,
--- 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. >:(
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.
penfold:
--- 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 ---
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.
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