Alfred Leitner - Liquid Helium II the Superfluid by Alfred Leitner (1963)
Source. Original source: www.alfredleitner.com.The bane of multicellularity.
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.
Ideally can be thought of as a one-way ticket gate that only lets electrons go in one direction with zero resistance! Real devices do have imperfections however, so there is some resistance.
First they were made out of vacuum tubes, but later semiconductor diodes were invented and became much more widespread.
There's not way to describe it as a classical function, making it the most important example of a distribution.
Applications:
- position operator in quantum mechanics. It's not a coincidence that the function is named after Paul Dirac.
Exams as a prerequisite for a degree are useless. Exams as part of a degree must be abolished. And degrees must be abolished. Ultimately the only metrics that really matter are money and fame. See also: motivation.
The only thing exams should matter for is as a screening tool to select people with specific abilities that you care about as an employer or principal investigator. If:then exams are useless for your purposes. then might as well just go by interviews (basically what all employers do already, though not PIs). Degrees are too course grained to mean anything to anybody. Employers and PIs likely only care about very few specific subjects.
- you have no idea about what the content of specific exams are (and you don't because they are all ad-hoc university secrets)
- or don't have a way to machine learn what grades correlate with your desired performance (you don't because where's the data?)
Once the question of an exam has been formulated, the usefulness of the problem is already been completely destroyed, because formulating the problem that matters is the most important part of things. And any problem with an answer, is useless to put effort into: give answers.
Furthermore, preventing people from searching for answers while answering an exam, AKA preventing "cheating", also makes absolutely no sense. In the real world, we want people to find answers as quickly as possible! We should be teaching people how to "cheat"! What we should teach them instead is what a fucking license is, and what you have to do to comply with it.
And if you must absolutely have exams, they must be open to anyone who wants to applies. Then people have to pay to take the exam, with subsidies for "official course takers", who are spending 100x more anyways due to not living with their parents.
And those exams must be applied by professional test application companies to ensure no cheating and to factor out the anti-cheat work, while still making the tests available to people anywhere.
A quote from Richard Feynman present in the book Surely You're Joking, Mr. Feynman chapter O Americano, Outra Vez!:
The only metric that matters is "to feel that you've satisfied youre curiosity". When one studies for that, it can take a lot more time to actually learn everything, because it is sometimes not as clear when you should stop. But it is the only way to go deeper.
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