This is extra bizarre to me, because for most purposes German law doesnt operate on a system of "legal precedent" the way countries which adopted the UK model do.
Am I missing something about Germany following a precedent system for patent/copyright or something, or is this even dumber than it sounds?
I didn't say anything about shutters, I said awnings. It's a testament to how much our society has forgotten about building effective homes that people think shutters are just as effective as awnings.
That said, yes, if possible, you should be installing an AC unit as well (and the awning will help make the AC unit more efficient.
This might be the coldest summer for the rest of your life. European summers are only going to get hotter, and more humid. Meanwhile, we have a pressing need to decarbonize our home heating solutions both for energy sovreignty and climate reasons.
Modern air-to-air heat pumps (i.e. aircon) are a pretty good solution for that. I think we're just going to have to work our way around this as a society. While many Europeans live in historic buildings that will require a lot more care, most do not, and installing aircon at least for homes with elederly people and young children provably will reduce unnecessary deaths during our now yearly heatwaves.
The rapid buildout of solar, and the rise of efficient air cons for electric home heating certainly makes it seem like a much less wasteful technology than before.
I still think though that people are severly underestimating the effectiveness of relative simple, low-tech options like awnings though.
The idea is that it's an alternative way of talking about vectors, rotations, and geometry in general. I.e. a replacement for the vector notation you learned that makes it operate more like how complex numbers are used.
I guess I'd say my point though is that the gauge structure is the mathematically interesting part of Maxwell's equations. (i.e. the fact that `F` is a closed differential form).
Without it, I think it'd be of significantly less mathematical interest because it'd lose almost all of its geometric properties.
More or less agreed. I think though that one reason the geometric product is so tempting is that if you take matrix representations of all of these objects, then the geometric product is literally just straightforward matrix multiplication.
Because of that, it just becomes so tempting to try and phrase everything you can in terms of this geometric product. I'm very sympathetic to the temptation, and I even think the geometric product has some great uses (it shows up a lot in some physics I do), and using it makes writing rotations a treat, but I think it's still vastly overemphasized by GA people.
I still don't really know what my favoured notation for differential geometry is, I find myself switching around so much.
> From a mathematician's point of view, yes, you should write the Maxwell field equations, at least to see it once, that way because you're showing a very low-level symmetry that even the differential forms approach doesn't get all the way to. Differential forms is a standard approach for general relativity, e.g. MTW.
While it's neat to write them all as one equation, I disagree that it's an enlightening perspective to learn. While it seems like writing Maxwell's equations in one equation instead of two is a step forward with even more symmetry, what is actually going on is that you are obscuring the most important part of Maxwell's equations: the gauge structure. Without this, it actually becomes much more hidden just how geometric electromagnetism is.
When you write Maxwell's equations as the pair `dF = 0`, `d*F = J`, the first of those two equations is exactly what tells you that this is a gauge theory, and thus may write `F = dA` where `A` is a vector potential. This vector potential then becomes the connection which defines a covariant derivative in a fibre bundle, and one then sees that charged particles follow geodesics now in spacetime, but in an enclosing fibre bundle. This is foundationally important to modern physics, and IMO obscured by writing Maxwell's equations as `∇F = J`
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n.b. I'm not a particularly big fan of differential forms either, I think it leaves a lot to be desired, and it's super awkward to constantly have to pull out Hodge Duals every time you want to do something that involves the metric, but I'm also unconvinced that geometric algebra is the answer here.
It's a very fun framework when you're learning it. It constantly feels like you're learning something extremely profound and useful, but I've also found that feeling to be a bit of a mirage.
Despite trying many times to make greater use of it, I've found that it often just makes a lot of actual physics work less clear, and with very little practical benefit.
There's times where it affords quite pretty notation, but often you have to actually unpeel all that notation before you actually do something with it. And what's the point of nice notation if none of your colleagues can even read it? The only time I ever really found that GA was actually a benefit to me was performing rotations.
There is ample competition from cars and planes, europe has one of the most dense and intensive highway networks in the world, and the most dense and intensive short-haul flight network in the world.
Rather, the trains in western Europe are so desirable that the prices don't need to be heavily subsidized in order to be fully utilized.
In most of western Europe, the main barrier to increasing train usage is the physical number of tracks and trains in operation. If prices were further lowered, there'd be nowhere to even put all the extra customers the subsidies would bring in. Therefore, if the governemnt is going to put money into the trains, the first priority is infrastructure expansions, not price subsidies
1) It's not a 10:1 ratio though, it's much more than that. These fare collection systems are very cheap relative to the money they bring in.
2) If there's sufficient money and will available to fund the transportation system to that level, then sure, that's great. But in most cases, I think it's better to just direct expansions in government train budgets towards expanding the network, not making it cheaper. Most people who drive cars don't drive because trains are expensive, they drive cars because there's no train at the time and place they want. Making trains cheaper doesn't address this problem.
No, it's not even close. Those fares don't cover the whole operation of the train system, but they actually go a long way to covering a very large chunk of it. The cost of operating the fare system is a rounding error relative to the sums of money talked about here.
Overall, DB Regio (the regional trains which are covered by the Deutschlandticket) has around a 89% punctuality score[1], which is very comparable to the Dutch numbers. There are certain hotspot regions though where the regional trains are truly fucked, but for most of the country they're totally fine and quite reliable.
It's mostly Germany's long-distance high-speed ICE trains which have punctuality problems (the much discussed 60% punctuality [2] score), but those are not covered by the Deutschland ticket, and the Netherlands has no comparable service to these trains anyways, so if one is envious of the state of Dutch trains, they can happily pretend that German ICE trains simply don't exist. In my experience though, the ICE's are a pleasure to ride.
Sidenote, but the ICE punctuality score is not really directly comparable with the Regional train scores, since they measure different things. The ICE score is about the passenger arriving at their final destination with less than a 15 minute delay including connections, whereas with the regional trains they don't have granular passenger level data, so they measure whether or not a train gets to the platform within 6 minutes of the scheduled time.
https://news.ycombinator.com/item?id=48672732