| General > General Technical Chat |
| "Veritasium" (YT) - "The Big Misconception About Electricity" ? |
| << < (364/396) > >> |
| adx:
--- Quote from: HuronKing on April 11, 2022, 08:03:10 am --- --- 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 --- End quote --- 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. --- Quote from: HuronKing on April 11, 2022, 08:03:10 am ---You keep accusing me, and others, of having axiomatic faith and 'convictions' and whining about belief systems with comments like this, ... --- End quote --- 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. |
| hamster_nz:
--- Quote from: adx on April 12, 2022, 04:55:40 pm ---Mathematics is (or is supposed to be) a rational belief system. --- End quote --- 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 |
| bsfeechannel:
--- Quote from: adx on April 11, 2022, 03:35:31 pm ---It's my entire point! Complex numbers as an engineering concept exist almost entirely separate from the sqrt(-1) definition. --- End quote --- 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. --- Quote ---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". --- End quote --- 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. |
| HuronKing:
--- Quote from: penfold on April 11, 2022, 11:09:19 pm ---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. --- End quote --- 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... ::) --- Quote ---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. --- End quote --- 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. --- Quote ---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. --- End quote --- You haven't understood the example. I'm not motivated enough to explain it further given what else I'm reading here. --- 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. --- End quote --- Yet there are some here who want to reduce both nature, and our math, to nothing more compelling than counting on fingers and toes. --- Quote ---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. --- End quote --- 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. |
| HuronKing:
--- Quote from: adx on April 12, 2022, 04:55:40 pm --- 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? --- End quote --- 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: --- Quote ---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. --- End quote --- -- Feynman 22-5 --- Quote ---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.) --- End quote --- 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. --- Quote ---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. --- End quote --- 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. --- Quote ---People who disagree with sqrt(-1) are disagreeing with a concept for the same reasons the name got invented - and that has meaning. --- End quote --- 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. --- Quote ---Unfortunately in trying to understand your questions here, I get more of a sense of belief and inability to see what I mean. --- End quote --- 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. --- Quote ---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. --- End quote --- "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. --- Quote ---All my objections to imaginary numbers in engineering disappear for polar notation (for obvious reason). I just prefer complex notation and operations. --- End quote --- 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. |
| Navigation |
| Message Index |
| Next page |
| Previous page |