Guys, is this also an “affirming the consequent” case? Because I see that if $V_{ij}$ is a function of only the distance between the particles, then we have that $F_{ji}=-F_{ij}$ and apparently the forces line along the line going the two particles. But did it also go in the other direction?
Eh. I think that's too harsh a tack. You can do theory in the absence of experiment, just based on physical principles. But you have to be very very very careful about what you're doing, and especially you have to be honest about that you're doing is high-risk.
I guess that's kind of true depending on what you're doing. Like if you're doing Riemannian geometry a lot of what you are doing is pretty physical, fundamentally a lot of results boil down to "given second order behavior of metric, derive properties of space" which kind of feels like what you do in mechanics a lot of the time. @Semi But idk much about physics
This video includes some visualizations of relativity, and it includes the rotation effect (though not as clearly as the rest, tbh): youtube.com/watch?v=JQnHTKZBTI4
@Semiclassical for example , i can set up different newton laws, by changing the formulas or by saying "for every action there is an opposing but UNequal reaction"
On the other hand, the underlying principle of momentum conservation does still hold (if you include the momentum contained in the electromagnetic field)
(Within the realm of classical mechanics, anyways. Within the realm of quantum mechanics there is a notion of 'negative mass' but the name is largely historical. See this blog post for some critical remarks on a hyped 'discovery of negative mass.')
If a rod is perfectly rigid, it would have to respond instantaneously on one end to being tapped on the other. But that'd allow for faster-than-light signaling.
The wave speed is slower than the speed of light, but it's far faster than I can perceive.
So I might as well just say that it's a rigid rod in that case. I know the model isn't physically absolutely correct, but it doesn't have to be to be useful and relevant.
It can be interesting to push that in the far other direction, to be sure: To think of ways that modern physics could be wrong, and try to figure out whether that could be observable.
Can $[a,b]$ reasonably be interpreted as, say, an interval in $\mathbb{R}^3$? Or did my professor somewhat bully me? (I use the word "bully" because there were instances of assured bad behaviour from her)
You could use $[a,b]$ to represent the line segment connecting two points $a,b$ but that's not standard notation and you would be expected to make that convention clear.
(especially since one has $\overline{ab}$ as defined notation for such a segment already)
@Semiclassical Yeah. By the way, she would even object to writing "for some/every blabla" right after some definition. Isn't that a stupid observation? I've seen actual papers written like that
Namely: "For the purpose of us learning how to write proofs, I'll expect you to always report definitions in the following way." But that only works if that's been made explicit.
my original question is like this Let $a, b, c, d$ belong to domain $R$ and satisfy $a + b = c$. Assume $d$ divides two of the elements $a, b, c$; prove that $d$ divides the third.
so if I assume $d \mid a$, may I write it as $a = kd$ for some $k \in R$?
anyone knows if this definition of a complemented lattice is valid? https://proofwiki.org/wiki/Definition:Complement_(Lattice_Theory)
I mean, if it's true then any bounded lattice $L$ is a complemented lattice since $\forall x \in L: x \lor \top = \top$ and $\forall x \in L: x \land \bot = \bot$ so the bounds are the complements for all elements in the lattice, so all bounded lattices would be complemented lattices.
But as a student, I'm wildly independent to the point of only ephemeral attendance, and tend not to involve myself in group projects when I can help it
I'd put myself at NG because I tend to act entirely outside my self-interest, and though I respect rules and norms, I see them as mutable and subject to personal interpretation, and in some cases may be safely ignored
as opposed to Extraverted, Sensing, Thinking, Judging
The issue I see most people have with MBTI is taking those letters at literal face value rather than looking at what the letters say about your supposed Jungian archetypes.
I find that the Jungian archetypes do to some extent describe my modes of interaction well, but that's not to say it's perfect, and it's also not to say that it's not a case of self-identification bias.
Guys ,I am really sorry but I have to post a damn chemistry question over here due to the non working of "The periodic table" ,tell me what is the answer for this following question :)
@TedShifrin: my solution might be ugly, but the original problem is quite natural, and comes from representing probability distributions as points on the simplex
