Without necessarily endorsing the article's ideas....I took this to be like the diamond-inheritance problem.
If service A feeds both B and C, and they both feed service D, then D can receive an incoherent view of what A did, because nothing forces B and C to keep their stories straight. But B and C can still both be following their own spec perfectly, so there's no bug in any single service. Now it's not clear whose job it is to fix things.
OOPs = "object-oriented programming", BUT it's a more restrained and thoughtful complaint than just "objects suck" or "inheritance sucks". He cabins it pretty clearly at 11:00 minutes in: "compile-time hierarchy of encapsulation that matches the domain model was a mistake"
I've seen a db mock work when 1) there was a small subteam in charge of the OR-mapping, schema structure, and included a DBA; and 2) also a design policy from the architect that all objects had to come out of factories. Under those specific circumstances, having the mock - used solely as a per-developer object cache imitating the factory interface - was critical for unblocking the people working on business logic and front-end.
I like this - nice playing around. We usually think of this kind of tree as having directed edges from parent to child, e.g. from set to element. In your graphs, you're erasing the direction of the edges, which uncovers a neat little symmetry that I never thought about before.
All the (non-limit) von Neumann ordinals are of the form X+1 = {X, {X}}, where X is the previous ordinal in the set. If you just look at trees of this form:
X+1: X <- node -> {X}, or X <- node -> node -> X
then you ignore the direction of the parent-child relation, you get this:
X+1: X -- node -- node -- X
So that's why your trees are symmetric as undirected graphs; and of course, every lower ordinal has its own version of this symmetry, which is also contained in the tree. All the large gaps between sections correspond to node--node edges of the larger ordinals. Kinda neat!
They are different: in the U.S. that's why "freedom of the press" is also written down in the First Amendment, and historically, that's exactly how the U.S. courts have interpreted the phrase "freedom of the press" - as a (pretty) general right for anyone to use any media technology they can access to spread any ideas they want. There are always some limits, but from the start "the press" meant "the printing press", not "institutionalized news organizations". It's a general technology-usage right, not a specialized right for a certain group. Everyone is allowed to do more than just talk, or even shout. People can have different opinions on how wise that right is, but in the US at least, you are indeed free to broadcast your nonsense to millions of people, if you have the resources.
Alice is taking a small unfair advantage of every member of the community at once. A community and its practices is a form of commons shared by the members, so it's vulnerable to the tragedy of the commons. If one member acts in a way that deliberately goes against the trust, that's inherently unfair to the rest of the members because it tends to push everything toward a breaking point. If her goal depends on the community's existence or function (which if it doesn't, why is she even around?), then whatever her goal, Alice has gone after it in a way that takes unfair advantage of everyone else's commitment to the system. Even if Alice's action doesn't cause a final breakdown, she's moved things in the wrong direction for her own purposes.
In fact, according to the Esolang Wiki [https://esolangs.org/wiki/List_of_ideas#Mathematics] , Gregory Chaitin apparently has built a Diophantine equation whose parameters encode an entire Lisp interpreter.
Yeah, this is a little bit subtle. Please ignore the lack of rigor below, but this is my understanding: They aren't looking at a particular polynomial like 4x + 3y = 2. That has a solution x=2, y=-2, but they don't really care about the exact value for (x, y), just that it's integers. They're more interested in the parameters: (4, 3, 2), and in general Ax + By = C. If you like, it's almost like hyper parameter tuning: what are the parameter settings for (A, B, C) where I can get this shape of equation to "work", e.g. give me acceptable x and y? A "Diophantine set" is a family of parameters that all work. It turns out you can think of "parameters of a given shape of Diophantine equation" as an exotic programming paradigm.
Fermat: x^N + y^N = z^N. The Diophantine set only has the number N=2, because Fermat's Last Theorem tells us that no other possible N will work if x, y, z have to be integers. This is just a finite set.
Other polynomial expressions work with an infinite number of parameter settings: Pell's equation is x^2 - N*y^2 = 1. In this case, every N that is not a square will work. This is an infinite set.
Because a lot of the parameter sets are infinite like this, the size of the parameter set are instead measured using big-O notation. For Fermat's Last Theorem, {N=2} is constant, so big-O(1). For Pell's equation, {N not a square} is O(N). For other Diophantine expressions, the parameter settings are O(N^2), or O(2^N), or any other growth function you want that's achievable with Turing machines.
And this is the essence of what MRDP proved. Robinson, Davis, Putnam, and Matiyasevich over several papers proved that if you could encode a set that grew roughly like O(2^N), you also could encode any other computable set in the parameters. Approximately, demonstrating an exponentially-fast-growing family of parameters for some specific Diophantine problem was enough for Diophantine problems as a whole to be Turing complete. Matiyasevich's clinching discovery was a concrete example using the Fibonacci numbers.
Fusion: Turbulence, plus Naiver-Stokes was known to be hard, plus adding in EM fields, plus the exothermic state change of the nuclei fusing introduces discontinuous jumps in the free energy.
Collatz: if you replace 1 and 3 with arbitrary parameters, Conway showed that this class of problems is undecidable, so any particular instance could be arbitrarily hard.
I read this as basically arguing that our filters throw up too many false negatives, like Kariko, in a high-risk/high-reward environment. It’s saying the cost of false negatives is way higher than the system realizes, and that’s because the system has drifted to be too much like the collaborative, incremental workplace that most of us live in. Typical work teams pay a high cost for false positives when hiring, so they guard against them at the cost of way more false negatives. The doesn’t work as well for moonshot fields.