Was trying to explain convolution (of functions) to a friend and I wanted to build a little picture. I typed more or less nothing into Claude and it gave me a fine web-app for demo'ing examples to my friend within minutes.
Three years ago this would have taken a minimum of three college graduates a couple days -- one to know the math, one to know the backend, and one to know the front-end. Maybe two of those could be the same person on a good day -- none of the topics is individually that hard -- but it's a lot together.
Yes, this is the crucial distinction. (I wish that articles criticizing PE were framed in terms of LBOs + bankruptcy-law instead, because that's the root of the policy problem.) Corporations can go bankrupt without risk to the human beings who are owners/investors in the corporation.
Note that from the lender's perspective, the risk is the same and in a perfect-information universe could be mitigated by charging higher interest. The problem for society is the externality that the business's services get worse.
I never really understood about PERM. Suppose I am a manager on a team and one of my employees is going through the PERM process.
I'm supposed to put out a job advertisement (but the job isn't real) for my employer. If an applicant passes the interview process, I don't have to hire that person (I probably can't - I don't have budget or permission from the organization). But I do have to honestly say if they have all the required skills -- I'm not permitted to say "wouldn't be a culture fit."
Nor do I have to fire my employee. But maybe my employee won't get a green card six years down the road.
1) Do I have any details wrong here? The one time I talked to a law firm about this they more-or-less refused to state the above outright, but answered all questions in this direction.
2) Doesn't this seem disrespectful to, among others, the applicants to the fake job?
The government enforces contracts, so it gets to choose which contracts it enforces. Without a functioning judicial system (and a law enforcement system to enforce its verdicts), a contract is a piece of paper.
Plenty of contracts benefit both parties but are bad for society as a whole, and if the government pre-signals which sorts of those contracts it will refuse to enforce, this is good for society.
Has anyone played Bean and Nothingness? Great game, but also a great Discord server for this problem, with lots of norms around spoiling. I've been disappointed in some board gaming forums moving to Discord (because it's hard to search for old knowledge), but for puzzle video games it's almost ideal.
If X is a smooth projective curve over an algebraically closed field k, then we can make a (huge, useless) abelian group Div(X) which is the set of formal sums of points on X. (The "free abelian group" on X).
It would be flippant to say Div(X) is an answer to your question, since it has nothing to do with geometry at all (we can form the free abelian group on any set). An element of Div(X) looks like \sum n_i P_i where n_i are integers and P_i are points on X, and they "add" in the obvious way. The sum doesn't "mean" anything. But we can get to geometry from it.
Inside Div(X) there is a subgroup, Div^0(X), of formal sums of points such that the set of coefficients is zero. Still nothing to do with geometry.
Inside Div^0(X), there is a very interesting subgroup, which is the set of "divisors of functions." Namely, if f is a rational function on X (meaning it's locally a quotient of polynomials), we get an element of Div^0(X) by taking \sum P_i - \sum Q_i where P_i are the zeroes of f and Q_i are the poles (caveat - you have to count them with multiplicity). This is an element of Div(X) but is not obviously an element of Div^0(X) -- this uses the fact that X is projective. Let's call the subgroup that comes this way Princ(X) (for "principal" divisors).
Now we get an interesting group that does have something to do with geometry, which is called Pic^0(X), by taking the quotient Div^0(X)/Princ(X).
Amazing theorem: there is a natural isomorphism from X to Pic^0(X) if and only if X is of genus one, i.e. an elliptic curve. (In general, Pic^0(X) is an abelian variety whose dimension is the genus of the corresponding curve.) This is why only elliptic curves (among the projective ones) are "naturally" groups. The relationship with the usual picture with the lines is that the intersection locus of the lines is the principal divisor associated with a functional that vanishes along the line.
Three years ago this would have taken a minimum of three college graduates a couple days -- one to know the math, one to know the backend, and one to know the front-end. Maybe two of those could be the same person on a good day -- none of the topics is individually that hard -- but it's a lot together.