* First, it's written in the typical style of AI slop.
* Second, a mathematician I know and trust writes "I went straight to the technical part (Sect. 3) and randomly checked one of the results (Theorem 3.14), finding that it is obviously false. (The category Comp mentioned in the theorem is formally introduced and makes sense per se, but it is certainly not additive with the proposed definition, as claimed in the statement of the theorem)."
* Third, another mathematician I know and trust writes "I spent almost an hour poking through here carefully to see where the more central claims begin to fall apart. Theorems 3.24 and 4.1 brazenly contradict each other, proving respectively that problems in P are homologically trivial and that all NP-complete problems are homologically isomorphic to all problems in NP. Even more to the point, the proof of 3.24 really shows the lie where it says "The detailed argument uses the functoriality of the computational homology construction and the fact that homology isomorphisms preserve the 'computational topology' of problems." The last claim is, naturally, not mathematically defined. The computational chain complex also appears not to be genuinely defined, as far as I can tell. I haven't compared to see what the author chucked into the formalized definition."
I'm starting to make videos for the University of Edinburgh. My first one was about this paper saying that neutrino oscillations may increase the formation of gold and other heavy elements in neutron star mergers:
You’re minding your own business when a police officer approaches you. They start asking questions, but something feels off. You ask for their name and badge number, but they refuse. What do you do?
As a citizen, you want to trust and cooperate with law enforcement, but you also have rights that must be protected. The question of whether police officers are legally required to identify themselves when asked is a complex one, with no easy answers.
In general, no, a police officer does not have to identify themselves even if you ask them—making it even more important to invoke your right to silence no matter who you think you’re talking to.
California Penal Code Section 830.10 states:
“Any uniformed peace officer shall wear a badge, nameplate, or other device which bears clearly on its face the identification number or name of the officer.”
However, there are a couple of key issues with this law that limit its effectiveness in ensuring police accountability:
The law only applies to uniformed officers, meaning that plainclothes officers or those working undercover are not required to wear any identifying information.
Even for uniformed officers, the law doesn’t explicitly require them to make their badge number or name easily visible or accessible to the public. An officer could potentially wear their identifying information in a manner that is obscured or difficult to read.
> An officer could potentially wear their identifying information in a manner that is obscured or difficult to read.
Yeah... but they could also not wear a badge. I doubt that'll fly
> or other device which bears clearly on its face the identification number or name of the officer.
Any reasonable court would find that wearing a badge in a manner that obscured the number or name would not be "clearly wearing" said badge. Is the officer an ethical person who makes a good faith attempt to follow the law they're hired to uphold, and will the court be reasonable are both questions that don't change what the law clearly expects and requires.
"Whatever the reason, the resistance to AC technology is making Europe a more impoverished civilization. It’s a major reason why Europe now feels shabbier and more hardscrabble than America..."
It feels shabbier and more hardscabble than America now? That's news to me.
It's a little late for a "wakeup call", no? More like "wake up, your house is on fire and behind your bedroom door it's a raging inferno out there".
> The economics profession should reflect on the fact that DOGE is proceeding without the input of economists because economists have downplayed the persistence and extent of government policy failures.
No, that's not the main reason why they're proceeding without the input of economists.
Hey, John — Matt Parker mentioned in one of his ellipse videos the fact that every elliptical ratio has its own pi-like constant. He just quickly rattles the fact off, but never delves into it. Do you know of any research into trying to characterize the family of pi? I mean, beyond its evil cousins.
For a circle, pi is the ratio of the circumference to its diameter. Every ellipse also has a circumference-to-diameter ratio. Well, two ratios, since ellipses have both major and minor diameters. You might think that there would be some kind of clever formula that let you calculate this ratio, but there isn’t! Instead, these pi-like numbers for ellipses are expressed as integrals:
Scroll down to “Complete elliptic integral of the second kind”. That is your search term for looking it up. It is kind of a surprise that there isn’t some neat formula for calculating the circumference of an ellipse. The formula given is:
C = 4 a E(e)
The function E(e) here can be calculated in a few different ways, but it is really just defined as an integral that measures the length of a single ellipse arc.
Here, e is eccentricity. E(0) therefore gives π/4 since a circle has eccentricity 0. E(1) also therefore gives 1. So the E(e) function goes from π/4 to 1 as e goes from 0 to 1.
In my "crackpot index", item 20 says:
20 points for naming something after yourself. (E.g., talking about the "The Evans Field Equation" when your name happens to be Evans.)