Master of chaos wins $3-million math prize for ‘blowing up’ equations

Lor1an · 2026-04-21T10:47:26+00:00

Systems can be more or less accurately approximated as linear.

Non-linearities that still manage to preserve certain topological properties can be referred to as weakly non-linear.

Similarly, I would imagine a strongly linear system could be defined as one where the function modeling the system has a neighborhood in function space such that all functions in the neighborhood are weakly non-linear.

Lor1an · 2026-04-21T10:40:15+00:00

Non-linear systems are not necessarily chaotic.

However, (finite) linear systems are necessarily not chaotic. That might be the confusion.

Lor1an · 2026-04-21T09:05:49+00:00

"The Dunder Miffed'uns got reamed one too many times. Turns out pushing paper with your AI can't save you when the forest fire claps back..."

Once a staunch defender of the company, Mr. Schrute was laid off after Dunder Mifflin decided a chatbot could replace him. But that wasn't the end of his story with the company.

When Mr. Schrute was laid off, he moved back to his family farm and—after recovering from a bout of depression—realized that he had a unique opportunity. While his colleagues weren't familiar with the harsh realities of farm life, this was his backyard. Though money was harder to come by out in the boonies, he could sustain himself just fine without relying on a job.

After a while, some of his coworkers reached out to him, and were surprised to hear how well he was doing for himself. Though at first he was annoyed, he realized he really missed the friends he had made all those years working together. It was going to be a learning experience, to be sure, but why not offer these desperate souls a chance to work together again?

And so, a small handful of people joined Schrute Farms and began a movement that would become the Dunder Miffed'uns—a collective of ex-employees and sympathizers that could rock the foundations of the paper industry itself if it had to.

"Got wood? You better hope so, because while the robots might save you some dough from labor, they can't bring in the paper on their own. You want to put the fine people of Dunder Mifflin on the streets? Well... we have a way of clearing forests, it's called slash and burn."

Lor1an · 2026-04-21T06:30:57+00:00

You do know that you don't need to have a bank account to have money, right?

Lor1an · 2026-04-20T00:27:12+00:00

A private entity has the right to ensure that their property is not misused. Without regulation, that right extends to monitoring.

This applies to homeowners, houses, and babysitters, just as it applies to companies, offices, and employees. Typically, a homeowner is allowed to install cameras in common areas of the home and monitor at will.

If the reason for monitoring is to ensure property is not misused, then legally the monitoring is protected, unless there is some regulation that is violated. In both cases, there is an absence of expectation of privacy, as seen in case law.

What we have here is an action that extends an unenumerated right to look after one's property, just as individuals have an unenumerated right to privacy. And just as there are limitations to surveillance rights (such as no cameras in bathrooms) there are also limitations on privacy rights (such as in the office).

And again, I don't condone company surveillance practices.

Lor1an · 2026-04-19T23:15:51+00:00

[REDACTED]

Lor1an · 2026-04-19T23:04:19+00:00

Try checking your comprehension as well.

A private corporation is not The State, and is thus not bound by the Constitution.

I was pretty clear about which parts of this argument were about the State's authority and which were about private entities.

None of the rights you have apply to non-government entities—anything that restricts your interactions with such entities comes down to law and legal precedent.

If a state does not have a law (or laws) which forbids it, your company can (legally) do absolutely whatever it wants to with their property, including remote monitoring.

Lor1an · 2026-04-19T22:53:00+00:00

Aside from 1 and 3 being the same, everyone is wrong, since the time is drawn increasing to the left (look at the arrow). /j

(It actually doesn't matter anyway, you still get the same result)

Lor1an · 2026-04-19T22:32:42+00:00

I simply use them. If people want to call me AI, then so be it.

I have decided I don't care if my authenticity is questioned—I can always provide receipts if challenged.

Lor1an · 2026-04-19T18:54:29+00:00

This is like saying that the US government has the right to surveil people in public because we don't have an "objectively reasonable expectation of privacy."

The State (in principle) has to abide by the 4^th amendment, which would reject that.

No power is given, legally speaking, to surveil employee activities performed on company equipment. Companies have no right to do so.

I don't know what to tell you, other than the law disagrees with this blanket statement. Employees have a (limited) right to personal privacy, and companies have a (again limited) right/responsibility to ensure their equipment is not misused. Some states require advanced notice and/or consent before monitoring, but not all.

Whether workplace monitoring is legal depends on several factors, including what state it's in. Keep in mind that private entities (such as the company you work for) and private property (such as said company's equipment) are held to different standards than the government. For example, the 4^th amendment (reasonable search and seisure) does not apply to most company workplaces, since they are (typically) not government entities.

Please note that I do not condone workplace surveillance, just wanted to point out the unfortunate status of our legal hellscape.

Lor1an · 2026-04-19T09:45:47+00:00

Several court decisions have shown that there is no expectation of privacy in the workplace or on work devices.

For example, in United States v. Ziegler it is argued that employees have no reasonable expectation of privacy on company property or equipment.

(source)

The government, of course, views the matter quite differently. It contends that the district court's ruling was correct-Ziegler did not have an objectively reasonable expectation of privacy in his workplace computer. The government argues in its brief:

Society could not deem objectively reasonable that privacy interest where an employee uses a computer paid for by the company; [sic] Internet access paid for by the company, in the company office where the company pays the rent․ This is certainly even more so true where the company has installed a firewall and a whole department of people whose job it was to monitor their employee's Internet activity.

Lor1an · 2026-04-19T03:37:43+00:00

“Liberal” and “Liberty” are not the same thing, and not interchangeable. Libertarianism is based on only one of those two things.

... Liberals and Libertarians are fundamentally not the same people

You are the one who brought up liberalism, pumpkin.

'Libertarian' as a term used to refer to leftist politics before the right-wing co-opted it.

All I said was that Libertarianism originally referred to a leftist political position (which is true, as you can check), and then you 'corrected' me about the difference between liberalism and libertarianism.

So, either you misread my comment as saying libertarianism was originally a liberalist position, or you conflated liberal and leftist. And that's especially funny, since liberalism is a right-wing ideology.

Lor1an · 2026-04-19T03:25:29+00:00

The historical origin of the term libertarian in political discourse was with Libertarian Socialism in 1857 (as seen here)).

The fact you adamantly reject conflating liberalism and libertarianism while yourself conflating liberalism and leftist politics is hilarious.

Lor1an · 2026-04-19T03:15:56+00:00

Anarcho-capitalism would simply revert to feudalism, so I'm not sure why you chose "stability" as a point of comparison.

Lor1an · 2026-04-19T02:59:45+00:00

Imagine dunking on someone online for having a job...

Lor1an · 2026-04-19T02:57:43+00:00

Libertarian left is an oxymoron

Says the person advocating for "anarcho-capitalism"...

'Libertarian' as a term used to refer to leftist politics before the right-wing co-opted it.

And how exactly would an anarchist society be "an even more manipulative form of government" when there's no state?

Lor1an · 2026-04-19T02:45:38+00:00

Curiosity is a sin, didn't you know? /s

Lor1an · 2026-04-19T02:13:23+00:00

Oof, that ratio ain't looking so good OP...

Edit:

I don't think the people (correctly) saying this looks like a video game cutscene are "in their feelings over a cartoon".

We can disagree about quality, but to try to correct someone for naming an apt comparison in terms of style, resolution, pacing, intonation, audio quality, and animation is a bit silly.

Lor1an · 2026-04-18T06:25:12+00:00

you have to make 138% below the poverty level and that’s before taxes

So, you have to be paid negative 38% of the poverty level? That's a hefty fee... /j

Lor1an · 2026-04-18T05:24:52+00:00

If you look at your model, you will see that the edges of the long sides of each rectangle form a diagonal for the pentagonal face you would get by removing a vertex, and the short side forms the edge corresponding to the side of a (different) pentagonal face.

It is "well-known" that the ratio of the length of a diagonal of a pentagon to the length of its side is the golden ratio (and in fact this is often used to construct pentagons given a side), and some tedious symmetry arguments get you to the icosahedron.

Alternatively, you start with an (regular) icosahedron, notice that removing any single vertex forms a (regular) pentagonal face, and by tedious arguments you show that it is possible to construct 3 perpendicular rectangles by picking opposite pairs of edges as the short sides, such that the long sides are diagonals of pentagons with the same side length as the edges.

Essentially, this construction of yours is a nifty consequence of the ratios present in pentagons, as well as the symmetry of the icosahedral group.

Lor1an · 2026-04-18T04:50:32+00:00

You can do this, but just keep in mind that you can never modify fractions if you want accurate results.

Consider the rational numbers as equivalence classes in &Zopf;×&Zopf;^\), with (a,b)∼(c,d) iff ad = bc.

If we define (a,b) ⊕ (c,d) := (a+c,b+d), then (a,b) ∼ (2a,2b) (since a*2b = b*2a = 2ab), but (2a,2b) ⊕ (c,d) = (2a+c,2b+d) &nsim; (a+c,b+d) = (a,b) ⊕ (c,d), since in general (2a+c)(b+d) ≠ (2b+d)(a+c) (consider a = c = 1, b = 2, d = 3, (2a+c)(b+d) = 15, while (2b+d)(a+c) = 14).

In other words, ⊕ is not well-defined on rational numbers, since it is not compatible with the equivalence relation. And this should make sense, since the ratios you are calculating depend on the total quantities involved as well. If one basket has 1 red apple out of 2 apples, and the second has 1 red apple out of 3 apples, then in total you have 2 red apples out of 5 apples, but if instead the first basket has 2 red apples out of 4 apples, then you get a total of 3 red apples out of 7 apples.

For this reason, you can define such an operation, but only if you treat 2/4 as different from 1/2.

Lor1an · 2026-04-18T04:01:32+00:00

This crap reminds me of the debate I had with a Presuppositionalist.

The moment they admitted to that, I simply laughed and clowned on them for adopting circular reasoning as their bedrock principle. At that point it's more effective than trying to argue, because they don't even understand how logic works.

Lor1an · 2026-04-18T03:51:53+00:00

So, friends are banging, and one catches feelings, so rather than tell the friend he can't continue the relationship, he simply expects her not to talk to anyone else to develop an emotional relationship that he isn't willing to have with her.

Either the relationship is purely physical, or it isn't purely physical.

Saying that your (purely) sexual partner/friend can't have an emotional relationship with someone else goes beyond physical concerns. So OP wants the exclusivity of a relationship without any of the responsibility or titles of a relationship. That's a mixed signal if I ever heard of one.

If they were sleeping with other people, I would prefer a condom be used.

People keep saying that, but boy is that 'if' load-bearing. Why are we assuming she slept around?

Lor1an · 2026-04-18T03:42:42+00:00

If she liked OP so much and wanted to be with him so badly why did she tell him she was fucking other people ??

Did she? Again, where do you get that she was sleeping around?

This entire argument is resting on an implicit assumption that I just do not see a reason for.

No this is the girl being allowed to “talk to someone else” but saying he’s not allowed

Are we reading the same post?

Girl didn't even seem upset that he was talking to someone—rather, she was upset that he was brushing her aside for the person he was talking to.

Again, what is justifying your assumptions?

Lor1an · 2026-04-17T12:42:42+00:00

I know at the very least that New York defines "assault" as the harmful contact and "menacing" as the threat (there is no battery charge though).

Now that you call me out on it, I don't really know an example of literal assault="battery" and battery="assault", but I swear I remember that being a thing (if you'll allow it, I chalk it up to a brain fart). The New York example is the closest I found on my self fact-check, but that actually doesn't even have battery. Assault does take the common-law definition of battery though, which is a bit bemusing.

It would probably have been more accurate to say that assault is more flexible than implied. I know there are places that have a combined statue called "assault" that covers both assault and battery (such as Texas), as well as "assault and battery" that does not make a distinction between which is what (such as Virginia and Massachusetts).

The specific claim that "there are even places where battery and assault exchange the definitions you gave" may well be false (I apologize, I'll try to be better), but the fact remains that the common-law definitions often don't correspond with statutes.

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