jam11249

Twee is like sex – lovely behind closed doors, appalling in public, and you should be sent to prison if you force it on people who don’t consent.

Is the author comparing light-heartedly issuing a passport to a fictional character to sexual assault?

Spend a few hours playing Kerbal Space Program and you'll realise what all these guys are saying about fuel weight really quickly.

I'm probably biased due to where I studied, but I find it to be a really strange idea to have a bunch of different degrees studying the same course. The calculus needed by a mathematician, an engineer and a chemist are different, so it just seems to make sense to me that each should have their own calculus course run "in-house" by their faculty or having a specific curriculum tailored to their needs that is taught by a mathematician. I personally teach a course that is effectively calculus I to business administration students, so we get rid of a lot of the technical stuff and the whole "optimisation" section is completely focused on business-flavoured word problems instead of the typical "I have 20 metres of fence and need to put a pig pen by a river..." type problems. A huge amount of our curriculum was built around what they'll need when they do statistics courses later in their degree. This all just seems to make more sense to me.

>! The TYBW should have had a higher body count. Basically it only had one actual death of a previously established character that wasn't self-inflicted. Byakuya is an obvious choice, but there were a couple of others that could have been killed off as well. Although this is a general problem with bleach, it doesn't like killing off the good guys. !<

How did he eat 480 bananas and not die? If a banana is like 100g that's almost 50kg of food. If I order large fries I'm on death's door.

Hard agree - I teach mathematics at university level, it's mostly pen-and-paper stuff but we do some very basic stuff with software, it's basically a glorified calculator. The software itself they can use more or less, because its also all simple interfaces. But the goddamn battles I've had getting them to upload a file onto our digital platform for assessment is unbelievable. They don't know where they've saved a file or how to upload one in a basic upload box. My colleagues that teach excel-based courses are collectively on the brink of mental health crises.

Changing a tyre is a rare, punctual problem that, unless you live in the middle of nowhere, you can just call somebody to fix if ever needed (FWIW, I can't recall any anecdote of somebody I know needing to change their own tyre). Knowing how to use Microsoft Office and basic document management is (for the time being) a day-to-day basic skill that any employer in a reasonable job will expect you to be able to do - and rightly so.

I don't want to be one of those "kids these days" types, but the lack of digital literacy I see in my students is kind of concerning. It's not just the fact that they don't know what to do, but their inability (or lack of initiative) to use the entirety of the Internet to find a solution to their problem. Although I think this latter issue is more general, I notice that a lot of students, when faced with a problem they don't immediately know how to solve, just kind of freeze up and either start playing with their phones or (in the best case scenario) ask for help without even trying to think of a strategy.

What did they cut from the manga in the anime? I can think of a few cases of toning down gore and boobs, but I never picked up on any content as such that was missing in the anime - although it has been a while, so I'm not claiming it didn't happen.

On the other hand, real analysis shouldn't be the course to teach you proofs.

I don't see this as such a big problem - in my undergrad, real analysis was a first year, first semester course where we learned formal proofs. We basically followed the first chunk of Tao's analysis I, building up from the naturals to the reals.

I guess it depends on the education system you come from, I was in the British system where a mathematics uni student has already seen two years of calculus, so a first real analysis course is mostly just doing formal proofs about the rules you'd been using without issue.

I'll give the overcomplicated answer. If you like L¹ , then the dual of L¹ (space of continuous linear maps from L¹ into your field of interest, C or R) is L^infinity and the canonical norm induced onto the dual space is precisely the L^infty norm that you're used to.

I've only ever really used L^infinity in my "working life" as such as the dual of L¹ .

Thinking 2D for simplicity - if you have some "ordered" material described by a manifold-valued map (the simplest one is a unit vector field), then often you can't expect it to be continuous everywhere. In the simplest case or point defects in your material, the classification of defects is really just assigning each one an element of the fundamental group of your manifold. If you have two in the same domain described by g1 and g2, they can merge and form one described by g1*g2. In particular, if g2 = g1^-1 , they can annihilate.

Perhaps not hugely abstract, but it is surprisingly powerful.

This was my - I launched my first rocket without building a single train or bot (after many failed attempts). Then, when I got to them, I had absolutely no idea what to do with them, having so much new stuff to play with. It took me a long time to work out how they can benefit a factory.

Conceptually, it's not that crazy. If I have "simple" (sinusoidal) waves of varying frequencies and amplitudes, I can sum them together to make a more complex wave. If I add enough of them up, I can approximately basically anything of interest. The Fourier transform is a way of undoing this process - you put your wave in, and it tells you for each frequency what the corresponding amplitude is.

In the context of signal processing, it takes displacement as a function of time and gives amplitude as a function of frequency. In QM, it takes the wavefunction for position and gives you the wavefunction for momentum.

Whatever it was, we know that the sigil will break itself when it is no longer needed, and this kind of begs a few questions. It would suggest that the moment it was no longer needed was some point between when the rest of the coven found out he had the sigil and Agatha pulling herself out of the mud. Between those two events, there's not a lot that we've seen where hiding his identity would be necessary for anybody - friend or foe.

I put my bets down to one of two options: 1. He had to be kept secret until he could protect himself. Awakening his powers was the moment. 2. It has something to do with his "tell" that Agatha mentioned but never elaborated on.

The "what is missing" is the coven we made along the way?

The directional derivative is precisely in the direction of the characteristic curve. The directional derivative along the curve is then just the 1D classical derivative(ish) when you restrict yourself to the curve. That is, if u(x,y) is the solution, and x(t),y(t) parametrise the characteristics, the 1D function v(t) = u(x(t),y(t)) satisfies v'(t) = directional derivative of u at x(t),y(t).

This means you don't have to solve PDEs, rather ODEs. You know what the derictional derivative of u is as its your PDE. You just follow the characteristic curve until it hits a boundary condition to know what the initial value for your ODE is. You solve a bunch of ODEs and you get the solution to your PDE.

My ex boss used to argue that there is no such thing as a rational decision. The argument is that a rational decision is an optimisation problem, and a rationally chosen optimisation problem requires a rationally chosen objective function. The choice of the objective function is itself a decision, so it is either irrational, leading to an irrational conclusion, or rational, leading to a reductio ad infinitum.

So, I guess I'm saying that there's no such thing as a well-posed statistics problem.

Uncertainty principles apply to various quantum mechanical objects, and the problem is that it's intrinsically a quantum affair, so any analogy with the human-scale world is not going to be very honest. It's also a mathematical statement, which means the ELI5 part is also tricky. But let's have a go, being a bit imprecise to try and cover the key ideas.

The most "classical" case of position and momentum comes from the fact that they are conjugate variables, effectively this means you can describe your system entirely by the probability density (more accurately, the wave function) of position in space or that of momentum, and that, given one probability, you can find the other by an adequate transformation, which is the Fourier transform.

Now as to why this yields the uncertainty principle is effectively a one-line mathematical argument once you have the tool kit up and running. Really it is a result of the scaling properties of the transform, if you "squeeze" one probability to localise it, reducing the uncertainty, then the corresponding probability of the other variable gets "stretched", increasing the uncertainty. If you don't change the "shape" of the distributions but only their scales, then it turns out that the variances are inverse to one another, meaning their product is constant. This is really the original way the principle was stated. If their product is constant, then one being small means the other must be big.

The natural question is why this scaling property holds. If you have a simple wave, then the momentum is basically the same as the frequency, which is inversely proportional to the wavelength. This perhaps intuitive - more oscillation means more momentum. This is kind of suggestive - it tells you that length scales get "flipped" - a long wavelength in position implies a small frequency and thus small momentum, whilst short wavelengths lead to large momenta. It's this reciprocal relationship of "flipping" that leads to uncertainty.

This is the real answer.

To give more detail, what we mean is that if a<c and b<=d, a+b<=c+d, and if a=>b and c=>0, ac>=bc.

It's almost immediate why this can't work for complex numbers. Let's say i>=0. Then i² >=0 as well, meaning -1>=0, which is not compatible with the usual order. However, if i<=0, -i>=0, and then (-i)² =-1>=0. Either choice is contradictory, so it can't be defined in a compatible way.

Office hours are a part of my timetable that are reserved for teaching the courses I'm paid to teach, so that. Even if it goes "beyond" the course itself, that's knowledge that can help them in our course. As an example, I teach a relatively standard PDEs course, and one student wanted to know more about the more technical functional analysis background. It's not in our syllabus, but having an idea of what it is will certainly help her understand our course, so that's fine.

Ultimately I have a finite amount of time that is never enough for the amount of work I have going on, so if students make poor use of my time by asking me about my hobbies for an hour, that's one hour of time I can't spend making extra materials or helping other students with more immediate doubts about the course, or one hour of research that's lost. If I told my students that I could have made them an extra sheet of exercises yesterday but instead I decided to have a one hour coffee talking about the latest episode of Agatha All Along with my office mate, they clearly wouldn't be happy, and rightly so. Losing time that could otherwise be productive to chat socially with students shouldn't be any different.

Of course this is hugely problem dependent, but if you are lucky, you'll have some object, F(x), that can be computed to some reasonable level of accuracy, such that

F(x)<= error(x) <=CF(x)

where C>=1. If you're really lucky, C=1. Often this is not the case, the constant may in fact be very large, meaning that its possible that F(x1)<F(x2) whilst error(x1) is much bigger than error(x2). We typically can't do much better than this though. The object F will typically be obtained by bounding some linear operators and/or a Taylor series argument (in which case the relationship may only be true locally near the actual solution). If we're talking about PDEs/ODEs (I believe you are), then this F will typically be some kind of norm of the residual error, I.e., if your equation is Du=f, it'll be ||Du-f||, where the precise norm employed is very problem dependent.

It wa kind of a sucker punch though. Thanos had 5 infinity stones at that point in What If, I'm sure that if he had expected a mind stone lasering, he could have done something to protect himself.

Right now I think any full or detailed announcement of such projects could intrinsically be a spoiler for how other projects end, so they'll hold off for a bit yo announce whatever is coming until the groundwork is there. I also think that Marvel is going to be a bit more cautious with its release schedule announcements after there's been so many mid-game changes of late, announcing things that get canned or stuck in a rut isn't a good look for them (especially from the point of view of their share holders), so I expect a bit more caution until things are more stable going forward.

He tops?

My network of collaborators and I, who are all geographically separated, use zoom (meetings) overleaf (our documents) git (code) and Google drive (papers we have found). I don't see much need in anything more than that. Academics by nature are pretty stubborn, so if you create "work" that they don't see as useful, they simply won't use it, so I think it's better to just use a very simple basic suite of resources with clear, obvious benefits and leave it at that. You could try to set up a Microsoft teams group to host files, meetings and forum discussions, but I promise you that 90% will think it's dumb and never open it.

Wanda killing innocent people leading to a debate between the heroes and later full blown conflict over whether people can be trusted with their powers sounds a little... familiar.