Your intuition is correct, it doesn't! A "3D hyperrope" is in fact just the surface of a ball[1], and it turns out that you can actually form non-trivial knots of that spherical surface in a 4-dimensional ambient space (and analogously they can be un-knotted if you then move up to 5-dimension ambient space, although the mechanics for doing so might be a little trickier than in the 1d-in-4d case). In fact, if you have a k-dimensional sphere, you can always knot it up in a k+2 dimensional ambient space (and can then always be unknotted if you add enough additional dimensions).
[1] note that a [loop of] rope is actually a 1-dimensional object (it only has length, no width), so the next dimension up should be a 2-dimensional object, which is true of the surface of a ball. a topologist would call these things a 1-sphere and a 2-sphere, respectively
Any time I am tempted to feel smart, I try to go and study some linear algebra and walk away humbled. I will be spending 20-30 minutes probably trying to understand what you said (and I think you typed it out quite reasonably), but first I have to figure out how... a 3D hyperrope is the same as a surface of a ball...
I'm not sure what you mean here. This is discussing a 1-dimensional structure embeded in 4-dimensional space. If you're not sure it works for something else, well, that isn't what's under discussion.
If you just mean you're just unclear on the first step, of laying the knot out in 2D with crossings marked over/under, that's always possible after just some ordinary 3D adjustments. Although, yeah, if you asked me to prove it, I dunno that I could give one, I'm not a topologist... (and I guess now that I think about it the "finitely many" crossings part is actually wrong if we're allowing wild knots, but that's not really the issue)
Every single definition that segments a real world set of continuous objects into discrete buckets has surprising edge cases. This is basically inescapable.
To steal a quote: All definitions are wrong. Some are useful.
As an American, is that the generally-accepted viewpoint now? That Brexit was a mistake? If so, do people feel like it was an honest mistake, or do people generally believe that the politicians and businesspeople who supported it were either incompetent or hoping to benefit personally at everyone else's expense? Something else?
I'm asking because I'd really like to believe that there's a point where a convincing majority of Americans will wake up and realize that Republican (and particularly Trump) politics are a sham and have been unabashedly so since at least the first Trump administration. I would like that, but I'm not hopeful at this point.
I'm not in England but in mainland Europe and yes, I don't know a single person who sees Brexit benefiting the Brits. It was all lies and pandering for politicians benefits.
Honest question because I'm ignorant, but did any (well, many/most since I'm sure there are outliers) mainland Europeans think it would benefit the British?
As an American generally uninformed on the manner, I only heard of pro-Brexit people in Britain.
Brexit was a vote by Britain to lose all influence in its largest export market and instead hamper its industries with dual regulation and increased barriers to trade. Nobody thinking rationally would think it was a good idea. The referendum passed because people were largely ignorant of what Europe actually is and because the referendum put a boring, complicated state affairs against a fill-in-the-blanks fantasy option.
The fact that they had literally no idea what would happen to Northern Ireland after Brexit tells you all you need to know about how well considered the idea was.
Part of this is down to the politicians who were running the show - David Cameron, the prime minister at the time, thought the referendum was a good way to put the issue to bed - you've had your vote, we're staying in, shut up.
He more or less directly said that they weren't going to make any concrete plans, because he thought the idea was so bad that they weren't going to spend the money on them, and because releasing explicit plans would probably just give ammunition to the 'leave' side. It certainly would have torpedo'd one of the major arguments of the 'remain' vote, which was that a vote to leave was a vote for uncertainty.
So in that way it was a self-fulfilling threat - you don't know what's going to happen because we refuse to make a plan!
> The referendum passed because people were largely ignorant of what Europe actually is
This too is a failure of politicians over several decades - the EU was always 'them', not 'us'. It was something that happened somewhere else. It was convenient to blame the EU when UK politicians couldn't or didn't want to fix something. MEPs were always pretty anonymous, unknown by local people who then (predictably) didn't turn out to vote in EU elections very much.
No, except every countries eu-exit party. Every europeen country has a ~20% block of people who want the ratatouille of leaving EU, no immigrants, etc. Luckily countries with a multi party democracy evade being hijacked by them so far.
To the rest of europe brexit looks like voting Donny back in: the bicycle-stick-frontwheel meme. Except brexit was a bit more contained so easier to laugh at, Donny siding with the enemy in our biggest armed conflict is no joke.
They stopped talking about it. They dropped the issue from their list. In my country they went to covid masks, siding with Russia in Ukraine (one of our ministers literally called zelensky a dictator) and now back to border controls I believe. It's like the "today I'm an expert in X" meme.
They always have like five taking points to whip their base in anger and it doesn't really matter what they are but they're always a bit lunatic.
I always find it so confusing - the same people that want group X (Palestinans, Kurds, Tibetans, Catalonia, etc....) to have their own government/country, hate that Brits want to control their own country.
You're talking about two very different sentiments. People see leaving the EU as a foolish decision. But Britain has every right to make that decision if it wants. I don't know of anyone outside of Britain who "hates" that they left (in the sense of feeling anger or offense).
In fact a lot of the sentiment tends to be more like "good riddance".
You're talking as though there were blue EU tanks rolling through the English countryside and bombers from Brussels flattening biscuit factories. Britain is not and was not oppressed, it's just a former imperial power with a heavily financialized economy that is no longer the biggest wheel in a larger regional economy.
Yeah the EU is totally to the UK like Israël is to the Palestians or Turkey to the Kurds. The EU put a wall around the UK and is slowly colonizing the area.
I live in a deprived area that voted overwhelmingly in favour of Brexit, despite almost everything good in the area being bankrolled by the EU development fund. It was very much not in our interest.
I think there were a good number of people to whom it was a coin toss: "maybe it'll turn out ok". I have friends in this group. Those, I suspect, have changed their mind. There have been no tangible benefits, and they weren't particularly attached to the idea.
For others it was a chance to give the establishment a kick in the balls. They were fed up with the stagnation and rot at the heart of our country. An honest assessment would have pinned the blame on conservatives that had been in power for a decade. But the EU made a convenient scapegoat for their own failings. By and large the media and politicians opposed Brexit. So the attitude was let's stick a knife in. Shake things up. I'm not convinced this group have changed their mind. Maybe some of them. But the Reform party promise to fix the whole mess (which they championed) in exchange for their votes. And I think they will get them.
For a more hardcore contingent it became an entire political identity. It's them, fighting for Britain's future, versus the "remainiacs" and the "media elite" etc who are frustrating the process. It would have worked out if people _just believed_ in it more! If we'd hard a harder Brexit. These people will never change their mind.
The politicians who told them (even for the time) quite obvious lies have not suffered any political consequences, far from it. A photo circulated on the night of Brexit where Farage was stood in front of a chart of GBP tanking while laughing. You'd think that would be his death knell! He likely shorted the pound for personal gain. Yet today he is more successful and more prominent than ever.
In short, I don't think there has been a reckoning. We are still dealing with the consequences, and likely will for a long time whether directly or indirectly
You convinced me! I wish I had multi-national committees of bureaucrats deciding what to do with the money of my countrymen, they know what's best after all
I am telling you that most of the good developments in my area - which is deprived and would not have had the funding otherwise - were through the EU regional development fund. Whatever you think of it, that is the reality.
> As an American, is that the generally-accepted viewpoint now? That Brexit was a mistake?
As a Brit who left the UK about 4 years ago but still keeps up on UK issues and news, I think this is overplayed. Sure, polls have showed the result would probably go a different way now, as it was somewhat marginal in the first place.
But the people shouting loudest about how much of a mistake it was are generally the same people who were shouting loudly about how much of a mistake it was going to be before the vote, who are (rightly or wrongly) still very bitter about it.
The generally accepted viewpoint on the ground seems to be "are we still talking about that?"
Which isn't so much an endorsement of the status quo, but a weariness of endlessly going over old ground and old battles, and general ennuis with the topic.
Politicians in the UK don't really discuss it much. The conservatives are still very pro-brexit because they own it, and because they are dancing towards the alt-right in an effort to end-run the 'Reform' party that's currently nipping at their heels (and who may as well be the UK branch of the MAGA franchise). Labour just don't want to touch it because they know that it's still divisive and they have enough other stuff to contend with. The most they're willing to say at the moment is that they would really like a better trading relationship with the EU and are pursuing closer trade deals. In the wake of Trump's tarriffs this seems to be accelerating as everyone else is scrambling to trade with whoever is more reliable than the US.
The media, AFAICT, have mostly lost interest too. The Guardian still runs some half-hearted pieces in the general direction every so often, but there's no serious 'rejoin' campaign even there. It doesn't help that many EU countries have since swung rightward and are taking anti-immigration stances now, so it's not such an obvious left-wing panacea as perhaps it once was.
The UK feels like a country in decline, and Brexit is probably a part of that, but while it casts a big shadow over everything it's not necessarily the most important problem the nation faces and it's not like there's an active political campaign to rejoin. It's been "kicked into the long grass" so to speak.
The UK public in general were never all that crazy about it, over the 47 years of membership the EU was always 'them', not 'us'. It was something that happened somewhere else, less important than local politics and local concerns. It was convenient to blame the EU when UK politicians couldn't or didn't want to fix something and needed a scapegoat. EU elections were always a sideshow with low turnout. For most it never felt like some aspirational thing, or relevant to daily life, just another layer of bureaucracy and a very remote one at that. British people were some of the least active users of freedom of movement to relocate, with more emigrating to the US, Australia and even China in recent years. It's easy to see why that created a situation where leaving was on the cards, and why the overwhelming response to it five years after leaving and almost a decade after the vote is "meh"
I wish people would stop trying to argue that the constitution affords due process to both legal and illegal residents like you are doing here. It does, but that’s missing the forest for the trees.
If all the government has to do is say “they’re here illegally” to get a free pass to do whatever they want to someone, then even legal residents don’t have rights. Due process is the entire mechanism behind which the government can establish something like illegal residency. As soon as you say Group A has the right to a trial and Group B doesn’t, calling someone a member of Group B is all it takes to subvert the entire legal process.
Isn't that what I just said? We already have the legal processes in place (based on the Constitution) to deport illegals in the correct (legal, safe, etc) way. The Trump administration is ignoring that existing process to score political points with their political base.
Couple that with their attempted demonization of the judicial branch and it's a recipe for a "first they came for the socialists..." situation.
Yeah, sorry, I didn’t mean to necessarily single you out.
I just hear the argument that the constitution gives both illegal and legal residents that right and conservatives simply respond that illegals shouldn’t have rights and that’s that.
It needs to be hammered in that due process is necessary even to establish the legality of their residency in the first place, otherwise the government can disappear whoever they want as long as they invoke the illegal immigrant boogeyman.
Many of the people currently being stripped of their rights and deported are documented, legal visa and green card holders or documented and legal asylum seekers.
Even illegal immigrants need to be deported through due process. That’s the entire part where the government is supposed to demonstrate that they are here illegally. We are currently skipping that part and essentially granting the executive branch unilateral authority to deport anyone to foreign labor camps as long as the press secretary says the words “illegal immigrant” or “MS-13”.
To make things even worse, these deportations are being overtly politically targeted. If you’re here on a legal visa and speak against this administration, they are making it clear that they will strip you of your visa and disappear you without a second thought and without an opportunity to defend yourself.
You are correct that the law is dead. You are embarrassingly mistaken about who killed it.
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