Japan has a fascinating culture. Wouldn't you say the same thing about video games? Which studio can sustain 6-7 years of active game development (The Legend of Zelda Breath of the Wild) exclusive for one console?
I think it's a weird way to learn math, and I learned it this way in school. Most of these courses just teach information memorization and recall. sin(x)^2 + cos(x)^2 = 1, etc.
I would start with something like Elementary Analysis: The Theory of Calculus, and work from there. You'll eventually arrive at the same place -- Calculus but from a much stronger mathematical foundation.
You learned using the AOPS books? Don't be fooled by the titles, these books exclusively use a proof-based approach to construct a pretty wide foundation around these topics.
AoPS are among my favorite math books, but they're definitely not proof-based or particularly rigorous in terms of formalism.
They do focus on complex problem solving, which is equally important. The key value-add of AoPS are interesting, often beautiful examples and problems.
However, they don't do proofs or formalism much. They don't do applications or show what math is useful for. And they completely, totally, and universally screw up units (you'll have problems trying to equate a length with an area and similar; that's true of their classes as well, and RSM is similar).
I don't think there's a one-stop-shop for math, though, which does everything right. AoPS is at the peak of their particular game (which is right in the name: problem-solving).
That's best complemented by:
- Something which does data, applications, visualizations, and storytelling well.
- Something which does early exposure / surface learning well
- Something which is more formal and rigorous in terms of proofs and derivations
- Something which touches on a broad set of interesting topics (graph theory, oddball parts of geometry, etc.)
- In 2024, I would add something which does computational mathematics well
Nothing I know of does all those well in a one-stop-shop.
I have not found that to be the case, the books I have read have gone into deep foundational detail to build up knowledge. Perhaps you're referring to Vol 1 & 2 of "The Art Of Problem Solving"? I haven't read them but from what I know they are a distillation of core concepts for students looking to do competitive maths.
It's confusing because that title is also the name of the publisher / website of the series of the books I'm reading.
PoE over CAN bus moves more complexity from EE world into software world. While Tesla currently has best auto software, this is still a very foreign and a different way of thinking/managing for traditional auto manufacturing. This won't be just using a different set of cables, it's going to flip their engineering departments upside down.
Power over Ethernet (PoE) is a technique for delivering DC power to devices over copper Ethernet cabling, eliminating the need for separate power supplies and outlets.
Existing aircraft will be wholly unable to compete on any route where LH2 aircraft operate, but it will take a long time to bring up the infrastructure for it. Expect it to appear first on select freight routes.
Oddly, H2 aircraft seem to be promoted with inboard tanks. The natural place for the tanks is in nacelles slung under the wings, for safety. (Hydrogen would not fit in the wings.) Hydrogen tanks in an enclosed cabin is a formula for disaster.
I am fairly sure this is due to the necessity of having pressurized cylindrical storage for the hydrogen. Fitting that kind of tank into the wings is going to be hard.
Tanks would be wholly impossible to fit into the wings. Thus, the under-wing nacelles. But pressure cylinders are a non-starter, because they are heavy. Expect to see, instead, insulated, unpressurized LH2 tanks.
The common criticism of LH2 economics is the energy required for liquification. Are you assuming that this is taken care of by overbuilding solar/wind and creating LH2 opportunistically?
Given the power requirements of flight — they're fuel efficient per passenger-kilometre, but they have a lot of passengers and go a long distance — planes are the only place[0] where I think "overproduction by nearby solar farms" just isn't going to be a thing.
OPEC paving their deserts with PV and synthesising fuel (whatever that is: hydrogen, Sabatier methane, aluminium for burning) or just exporting that electricity along a 2m^2 cross section solid aluminium rod to the other side of the planet? Sure, plausible.
[0] I was going to say "and rockets", but then I realised we don't launch anything like as many rockets as we fly planes, so even then rockets might still be running on green hydrogen or methane derived from it.
Notably, SpaceX is making no visible effort to synthesize methane for their cans. The only gesture in that direction is an announced plan to buy a pre-fab methane refinery that could possibly be adapted to run Sabatier; but no hint at a solar farm to power it, or a place to put one. I guess they could build one across the border in Mexico? CH4 for Cape Canaveral is a separate problem. More likely the refinery will just purify mined LNG.
Solar and wind farms supplying international airports would probably need to send power via HVDC transmission lines. But, yes, the airports will need much more than just overage from the farms, and probably booster shipments of LH2 from farms in the tropics, besides. Imagine how big must be the project of refining, transporting, storing, and distributing kerosene to gates, today. Yet it is made almost invisible.
> Existing aircraft will be wholly unable to compete on any route where LH2 aircraft operate
? Are you suggesting this will be a result of regulatory action? Since it would most likely be more expensive for the first decade, even if I gave you a tap on the airfield labelled "free H2"
It is because the very large difference in fuel weight for a flight leaves radically increased capacity for carrying paying freight. As LH2 produced on-site at airports gets cheaper than Jet-A fuel, the gap widens.
Volume is cheap, on aircraft. If a normal freighter today takes off with 25t of kerosene, the similar-sized LH2 craft needs only 10t of LH2. That means it can take an additional 15t of paying cargo.
That tendency will delay the transition. But the big economic benefit arises from being able to carry 40% more cargo because the fuel is lighter. Passenger aircraft capacity is maxed out when the seats are full, now that carrying freight in the same aircraft is not allowed. Also, it will take a long time for safety worries to be satisfied.
I think hydrogen for aviation is probably a dead end. I suspect the long term solution for aviation, at least long haul, is biofuels. Battery tech is edging into the realm where it could be used for short haul flights, but we have quite a ways to go before you'll be able to fly across the Pacific, or even Atlantic, on a single charge with reasonable passenger comfort.
Biofuels today have issues, but there's no fundamental problem preventing them from being green. It's just a side effect of shoehorning them into our existing agriculture systems.
In the future when we have more solar power than we know what to do with during the day it may become economical to run the Sabatier reaction with hydrolyzed seawater and atmospheric CO2 to make methane, which can be burned in a lightly modified aircraft turbine.
What do you mean? The fuel itself should be carbon neutral, even if it requires extra energy to create. I don't see any reason you couldn't make carbon neutral bio fuel, although I'd net on syngas instead.
Growing food and converting it to fuel is not carbon neutral. Farming is very resource intensive at the scales needed. In fact, it is literally the same idea as carbon capture, but via biology instead of synthetic. As a result, it is entirely a bad idea.
A catch is that hydrogen does become much safer in high-pressure tanks, because, when such tanks are breached, hydrogen escapes so fast that it can't react with oxygen fast enough to burst into flame. To prove this, Toyota literally shot their hydrogen tank with .50 cal[1].
Practically no one died in the Hindenberg disaster. There were more people injured than died. Most people involved just walked away from it. It was televised spectacle much more than a factual tragedy.
(It's a bit like saying we shouldn't use AC power because look what Edison did with those poor elephants. It's interesting anti-technological propaganda that made sense socio-politically at the time but isn't that useful to today's discussions.)
the problem isn't the policy, it's that when they repealed it China was facing the same issues as Japan, Taiwan, the US, Europe, etc. which is that no one is having kids.
Like Japan never had that law and is still having serious consequences
Electric cars are significantly easier than ICEs to develop electrically and mechanically. Car companies are notoriously bad at writing software. These are orthogonal statements.
I wonder if lack of empowerment is partially caused by unnecessary layers in administration. Admins are there "support" teachers but that probably also takes away some of the job aspects that feel "empowering."
Definitely part of it. Public schools, like many businesses and institutions, are full of administrative positions with inflated salaries who do some vaguely defined job.
