You should have typed up Equation (3.1.3) just for context
Anyway, it is that, while each individual $\nabla$ is "non-linear" in $\omega$ (as in, the 1-form's functional, position dependence, over a region, not just at point p), the difference $\tilde\nabla-\nabla$ is linear in that dependence, only depending on the 1-form's value at p alone.
@SillyGoose what you seek in a text is vastly opposite of what other people would be seeking in a text. A great exposition to others is not so for you. Great expositions for you ain't readable for most of humanity.
@Relativisticcucumber you should be able to make the multipole expansion yourself and show that the dominant behaviour at infinitely far away is the term that you expect.
@Relativisticcucumber for people who can just make guesses, sure. But the vast majority of hoomanity require some hand-holding, and if said hand-holding can just be done by oneself doing the computations by hand, that should totally be acceptable. Complain if the professor only accepts non-computational solutions
My fear is that it’s a timed exam and if he expects me to be able to just see by inspection I seem to be missing the learning objective by doing brute force computations
@Relativisticcucumber But technically you can easily "read off". Like, pick the centre of symmetry and then compute the moments. That is, sum of charges = 0 means no monopole term. Sum of charges multiplied by position vector relative to this centre of symmetry = 0 means no dipole term, etc.
@Relativisticcucumber In any timed exam you are supposed to skip questions that require a lot of computation and come back to them later.
> In the case of the ways in which they are produced, this is because some animals are produced without copulation and some as a result of intercourse. Of those produced without copulation, some are produced from fire, like the little creatures which appear in ovens, some from stagnant water, like mosquitoes, some from wine turning sour, like gnats, some from slime, like frogs, some from mud, like maggots, some from donkeys like dung beetles, some from fruit, like the gall-insects which come from wild figs, some from rotting animals, like bees which come from bulls and wasps which come from…
> Further, when we have stared for a long time at the sun and then bend over a book, we think that the letters are golden and moving around.
It's extra wild because it's from Sextus Empiricus, the man claiming that he only takes extremely obvious facts at face value and will doubt anything else
but apparently some idea he heard a guy say about bees is good enough
Well, the list is very long; each alone is incredible today, but if you consider that this was their best understanding of the time, and that they themselves could have seen it so, then you would also understand that the combination of them all make for a certain picture that life is miraculous
He is using the behaviour of a dog as an argument, and the translator refers to it as a "doggy syllogism" :)
> In our individual peculiarities we differ in such a way that some people digest beef more easily than rock-fish, and get diarrhea from weak Lesbian wine.
@qwerty I just remembered Rob's message here on Physics SE titled "Alphabet questions versus Dinosaur question". It is very appealing and delightful reading.
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@Mr.Feynman Possible answer of "can you do me a favor?" is "It depends."
@Mr.Feynman I think in that case they expect you to ask what's up or what is it, not commit. I guess the etiquette changes slightly when you're irl or 1:1 imo because it's less easy or expected to just ignore something you can't address
@qwerty I'm easily triggered by that. I'm the kind of person who replies "yes, I can" if someone asks "Can you open the window?" and then I stay still :P
@qwerty in your undergraduate years when you used to struggle with physics/math problems so have you faced times when you get discouraged a lot and questioning whether you're good enough to do it or not?
@Mr.Feynman can I say you're like a person who picks up a call and say "why you called me?", "come to the point"?
@qwerty then you were at nice place. Once I went to my university professor to take his help in an integral and I showed him my attempts and he said "we can't do every integral. And other discouraging stuff" then I asked that integral and RobJohn did that.... I admit that that university is literally not for studying, it is just for giving people degree.
@qwerty sorry? wasn't just struggle means it was more than that? do you enjoy evaluating integrals and doing programming challenges as can be found on Project Euler or Advent of Code?
@Mr.Feynman I once read first chapter of his book "Surely, you're joking Mr Feynma" and that really surprized me. Lol and his both Tea and Coffee joke then the lady said "Surely, you're joking mr feynam."
@LuckyChouhan I mean you would probably be more likely to completely quit or have thoughts of quitting if you only had negative experiences with the work + people , if you only struggled and never had moments where it wasn't just struggling
@qwerty I had many 'Aha!' moments when I wrote the code for a problem which I think is a nice problem. And read George Polya's book and had some more advice from MSE, I realized that "Avoid skipping around between problems, as it undermines one's ability to think deeply." (PS Here the term nice problem means the problem which I think is challenging for me and interest me)
@Mr.Feynman "Should I kill myself or have a cup of coffee?" ~ Albert Camus
I dunno I get the whole "oh no everyone is smarter than me" but frequently enough in academia I also get the thought "omg you're all a bunch of idiots... why are you saying that"
it never happens on stackexchange though - well, not never, but rarely
Like, when you feel like an idiot you're comparing to someone who's performed or who's performing better than you; in the other case the opposite
So, I will admire and look up to someone who's much more knowledgeable - also feeling inferior and experiencing the thought that you've mentioned. I will have the perception of not "being good enough", but that doesn't mean that I will consider anyone around me better than me
In a very schematic way, the process - at least for me - is about setting the bar very high, so that after I've set it, everyone will look "dumber" in my eyes, not just myself
@RyderRude people have different backgrounds, life circumstances and other things though. that's the other thing to keep in mind, so sometimes the comparison might be unfair or illplaced. it can be hard to directly or fairly compare ability or even just knowledge. so I guess that's a counterargument.
Ok, one thing just to make your life easier @imbAF everytime you have a slashed $a$, replace it with a $\gamma^\sigma$ (making sure the indixed is not already used) in proving the identity
Like, the one you've just proved is really $$\gamma^{\mu}\gamma^{\nu}\gamma_{\mu}=-2\gamma^{\nu}$$
@Mr.Feynman I just read your about on MSE. Would you name any concept or problem which you liked a lot in math or that helped you to understand something better?
@LuckyChouhan I don't have a specific instance now, but there are some situations in which I'm not compatible with the physicists' use of language, which tends to be ambiguous or incomplete
So I find that learning math and doing things in the math way can help understanding, if anything to isolate where the true physics stands and where the problem is purely mathematical
@LuckyChouhan No. I'm the equivalent of a sloth :P
@Mr.Feynman See this is an instance where I am not sure what to do: I proved earlier that $\not a \not b=ab-i\sigma^{\mu\nu}a_\nub_\nu$. Now I plan on substituting this expression in here $\gamma_\mu \not \not b\gamma^\mu$/ But I assume the indices should be different than $\mu$ in the expression right?
One of Feynmans greatest achievement is tricking people who wanted to study physics into thinking, that if they try really really really hard, even if ordinary, they will be able to achieve the same things he did :D
@Mr.Feynman nice, you know few days ago someone wrote here that this physics can't solve 3 body problem, that can't solve 2 body problem and so on.. but now I can't find that. And yeah I remember you told me that you're learning Japanese before :P
Progress in physics: Newtonian mechanics can't solve the 3 body problem Relativistic mechanics can't solve the 2 body problem Quantum mechanics can't solve the 1 body problem String theory can't solve the vacuum
Yeah, it would be $$\gamma^\mu\gamma^\alpha\gamma^\beta\gamma_\mu=2g^{\mu\alpha}\gamma^\beta\gamma_\mu-\gamma^\alpha\gamma^\mu\gamma^\beta\gamma_\mu=2g^{\mu\alpha}\gamma^\beta\gamma_\mu-\gamma^\alpha 2g^{\mu\beta}\gamma_\mu+\gamma^\alpha\gamma^\beta\underbrace{\gamma^\mu\gamma_\mu}_{4}$$
Now $2g^{\mu\alpha}\gamma^\beta\gamma_\mu=2\gamma^\beta\gamma^\alpha$
when in the expression you have: $\gamma^\mu\gamma^\nu$ How do you substitute this:$(2g^{\mu\nu}-\gamma^\nu\gamma^\mu)$ or $(2g^{\nu\mu}-\gamma^\nu\gamma^\mu)$
